ACCUPLACER Quantitative Reasoning, Algebra & Statistics Quiz: Setting Up Linear Equations
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Setting Up Linear EquationsQuestion 1 of 20

A rental company charges for a leaf blower based on the equation C=8h+15C = 8h + 15, where CC is the total cost in dollars and hh is the number of hours the blower is rented. A second company's price is described as a $25 flat fee plus $6 per hour. A customer wants to find the number of hours, hh, for which the cost from both companies is the same. Which equation should the customer solve?

8h+15=6h+258h + 15 = 6h + 25
8h+6h=25+158h + 6h = 25 + 15
8h+15=25h+68h + 15 = 25h + 6
15−8h=25−6h15 - 8h = 25 - 6h
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ACCUPLACER Quantitative Reasoning, Algebra & Statistics Quiz

ACCUPLACER Quantitative Reasoning, Algebra & Statistics Quiz: Setting Up Linear Equations

Practice Setting Up Linear Equations in ACCUPLACER Quantitative Reasoning, Algebra & Statistics with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Setting Up Linear Equations, giving you a quick way to practice the rules, question types, and explanations that matter most for ACCUPLACER Quantitative Reasoning, Algebra & Statistics.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

A rental company charges for a leaf blower based on the equation C=8h+15C = 8h + 15, where CC is the total cost in dollars and hh is the number of hours the blower is rented. A second company's price is described as a $25 flat fee plus $6 per hour. A customer wants to find the number of hours, hh, for which the cost from both companies is the same. Which equation should the customer solve?

  1. 8h+15=6h+258h + 15 = 6h + 25 (correct answer)
  2. 8h+6h=25+158h + 6h = 25 + 15
  3. 8h+15=25h+68h + 15 = 25h + 6
  4. 15−8h=25−6h15 - 8h = 25 - 6h
Explanation: To find when the costs are the same, we must set the expression for the first company's cost equal to the expression for the second company's cost. The first company's cost is given as 8h+158h + 15. The second company's cost is a $25 flat fee plus $6 per hour, which is represented by 6h+256h + 25. Setting them equal gives 8h+15=6h+258h + 15 = 6h + 25.
  • B incorrectly combines the hourly rates on one side and the flat fees on the other, rather than equating the total cost expressions.
  • C incorrectly associates the $25 fee with the number of hours for the second company.
  • D incorrectly subtracts the hourly cost from the flat fee for both companies.

Question 2

A total of $8,000 is invested in two separate accounts. One account earns 3% simple interest annually, and the other earns 5% simple interest annually. The total interest earned from both accounts in one year is $340. If xx is the amount invested at 3%, which equation can be used to find xx?

  1. 0.03x+0.05(8000−x)=3400.03x + 0.05(8000 - x) = 340 (correct answer)
  2. 0.03x+0.05(x−8000)=3400.03x + 0.05(x - 8000) = 340
  3. 0.03x+0.05y=3400.03x + 0.05y = 340
  4. x+(8000−x)=340x + (8000 - x) = 340
Explanation: Let xx be the amount invested at 3%. The interest earned from this account is 0.03x0.03x. Since the total investment is $8,000, the amount invested in the other account at 5% is 8000−x8000 - x. The interest from this second account is 0.05(8000−x)0.05(8000 - x). The sum of the interest from both accounts is $340, so the equation is 0.03x+0.05(8000−x)=3400.03x + 0.05(8000 - x) = 340.
  • B incorrectly sets up the amount in the second account as x−8000x - 8000, which would be a negative value.
  • C is an equation with two variables and does not use the information that the total investment is $8,000 to express yy in terms of xx.
  • D incorrectly sets the sum of the principal amounts equal to the interest earned, not the total principal.

Question 3

A chemist needs to create a 20-liter solution that is 35% acid. To do this, she will mix a solution that is 25% acid with another solution that is 50% acid. If xx represents the number of liters of the 25% acid solution, which equation can be used to determine the value of xx?

  1. 0.25x+0.50(x−20)=0.35(20)0.25x + 0.50(x - 20) = 0.35(20)
  2. 0.25x+0.50(20−x)=0.35(20)0.25x + 0.50(20 - x) = 0.35(20) (correct answer)
  3. x+(20−x)=0.35(20)x + (20 - x) = 0.35(20)
  4. 0.25(20)+0.50x=0.35(20+x)0.25(20) + 0.50x = 0.35(20 + x)
Explanation: The total amount of acid in the final mixture must equal the sum of the amounts of acid from the two initial solutions. The amount of acid from the 25% solution is 0.25x0.25x. Since the total volume is 20 liters, the volume of the 50% solution is 20−x20 - x liters. The amount of acid from this solution is 0.50(20−x)0.50(20 - x). The total amount of acid in the final 20-liter solution must be 35% of 20, which is 0.35(20)0.35(20). Therefore, the equation is 0.25x+0.50(20−x)=0.35(20)0.25x + 0.50(20 - x) = 0.35(20).
  • A incorrectly represents the volume of the 50% solution as x−20x - 20.
  • C equates the total volume of the solutions to the total amount of acid, which is incorrect.
  • D incorrectly calculates the amounts of acid and the final volume.

Question 4

A cell phone plan costs $45 per month, which includes 5 gigabytes (GB) of data. There is an additional charge of $12 for each gigabyte of data used over the initial 5 GB. Last month's bill was $81. If gg represents the total number of gigabytes used, and g>5g > 5, which equation represents this scenario?

  1. 45+12g=8145 + 12g = 81
  2. 45+12(g−5)=8145 + 12(g - 5) = 81 (correct answer)
  3. 45+12(5−g)=8145 + 12(5 - g) = 81
  4. 45g+12(g−5)=8145g + 12(g - 5) = 81
Explanation: The total bill consists of the flat fee ($45) and the overage charge. The overage charge applies only to the data used beyond the initial 5 GB. This amount of data is g−5g - 5. The cost for this extra data is $12 per gigabyte, or 12(g−5)12(g - 5). The total bill is the sum of the flat fee and the overage charge, so the equation is 45+12(g−5)=8145 + 12(g - 5) = 81.
  • A incorrectly applies the overage charge to all gigabytes used, not just those over the limit.
  • C incorrectly calculates the number of overage gigabytes as 5−g5 - g, which would be negative.
  • D incorrectly multiplies the flat fee by the number of gigabytes.

Question 5

Maya is twice as old as her cousin Ben. In 8 years, the sum of their ages will be 43. If bb represents Ben's current age, which equation can be used to find Ben's age?

  1. 2b+(b+8)=432b + (b+8) = 43
  2. b+8+2b=43b + 8 + 2b = 43
  3. (2b+8)+(b+8)=43(2b + 8) + (b + 8) = 43 (correct answer)
  4. 2(b+8)+(b+8)=432(b+8) + (b+8) = 43
Explanation: Ben's current age is bb. Maya's current age is twice Ben's, so she is (2b). In 8 years, Ben's age will be b+8b + 8 and Maya's age will be 2b+82b + 8. The sum of their ages in 8 years will be 43. Therefore, the equation is (b+8)+(2b+8)=43(b + 8) + (2b + 8) = 43.
  • A correctly states Maya's current age but only adds 8 years to Ben's age, not Maya's.
  • B adds 8 years only once, failing to account for both people aging by 8 years.
  • D incorrectly calculates Maya's future age by doubling Ben's future age, instead of adding 8 to her current age.

Question 6

A water tank currently holds 200 gallons of water. A faucet is turned on, adding water to the tank at a rate of 15 gallons per minute. At the same time, a drain is opened, removing water at a rate of 5 gallons per minute. Which equation represents the amount of water, WW, in the tank after mm minutes?

  1. W=200+(15−5)mW = 200 + (15 - 5)m (correct answer)
  2. W=200+(15+5)mW = 200 + (15 + 5)m
  3. W=(200+15−5)mW = (200 + 15 - 5)m
  4. W=200−15m+5mW = 200 - 15m + 5m
Explanation: The initial amount of water is 200 gallons. The net rate of change is the rate water is added minus the rate it is removed: 15−5=1015 - 5 = 10 gallons per minute. The total change in water over mm minutes is (10m). The total amount of water WW is the initial amount plus this change, so W=200+10mW = 200 + 10m, which is equivalent to W=200+(15−5)mW = 200 + (15 - 5)m.
  • B incorrectly adds the rates, which would be the case if two faucets were filling the tank.
  • C incorrectly multiplies the initial amount by the number of minutes.
  • D incorrectly subtracts the fill rate and adds the drain rate.

Question 7

A punch recipe calls for 3 parts cranberry juice to 5 parts ginger ale. If a total of 40 cups of punch is to be made, which equation can be used to find the number of cups of cranberry juice, cc, needed?

  1. c+53c=40c + \frac{5}{3}c = 40 (correct answer)
  2. c+35c=40c + \frac{3}{5}c = 40
  3. 3c+5(40−c)=403c + 5(40-c) = 40
  4. c=35(40)c = \frac{3}{5}(40)
Explanation: Let cc be the cups of cranberry juice and gg be the cups of ginger ale. The ratio is c/g=3/5c/g = 3/5, which can be written as g=53cg = \frac{5}{3}c. The total amount is c+g=40c + g = 40. Substituting the expression for gg into the total equation gives c+53c=40c + \frac{5}{3}c = 40.
  • B incorrectly reverses the ratio when solving for gg.
  • C incorrectly uses the ratio parts as multipliers for the volumes.
  • D incorrectly assumes cranberry juice is 3/5 of the total; it is 3/8 of the total (3 parts out of 3+5=8 total parts).

Question 8

Jamal has a collection of dimes and quarters with a total value of $13.15. He has 11 more quarters than dimes. If dd represents the number of dimes, which equation represents the total value of the coins?

  1. d+(d+11)=13.15d + (d + 11) = 13.15
  2. 0.10d+0.25(d−11)=13.150.10d + 0.25(d - 11) = 13.15
  3. 0.10d+0.25q=13.150.10d + 0.25q = 13.15
  4. 0.10d+0.25(d+11)=13.150.10d + 0.25(d + 11) = 13.15 (correct answer)
Explanation: The value of the dimes is 0.10d0.10d. The number of quarters is 11 more than the number of dimes, which is d+11d + 11. The value of the quarters is 0.25(d+11)0.25(d + 11). The sum of these values is the total value, $13.15. Therefore, the equation is 0.10d+0.25(d+11)=13.150.10d + 0.25(d + 11) = 13.15.
  • B incorrectly subtracts 11, representing a situation where there are 11 fewer quarters than dimes.
  • C is an equation with two variables and does not use the relationship between the number of dimes and quarters.
  • D adds the number of coins, not their monetary value.

Question 9

An unknown temperature scale, Scale X, is linearly related to the Celsius scale. A temperature of 10°C corresponds to 40°X, and a temperature of 30°C corresponds to 90°X. If cc represents the temperature in Celsius, which equation correctly relates it to the temperature in Scale X, xx?

  1. x=0.4(c−10)+40x = 0.4(c - 10) + 40
  2. x=5(c−10)+40x = 5(c - 10) + 40
  3. c=2.5(x−40)+10c = 2.5(x - 40) + 10
  4. x=2.5(c−10)+40x = 2.5(c - 10) + 40 (correct answer)
Explanation: A linear relationship can be described by the point-slope form y−y1=m(x−x1)y - y_1 = m(x - x_1). Let cc be the x-axis and xx be the y-axis. The slope mm is ΔxΔc=90−4030−10=5020=2.5\frac{\Delta x}{\Delta c} = \frac{90 - 40}{30 - 10} = \frac{50}{20} = 2.5. Using the point (10, 40), the equation is x−40=2.5(c−10)x - 40 = 2.5(c - 10), which rearranges to x=2.5(c−10)+40x = 2.5(c - 10) + 40.
  • B incorrectly calculates the slope as 5.
  • C reverses the roles of xx and cc in the point-slope formula.
  • D uses the reciprocal of the correct slope.

Question 10

At a movie theater, adult tickets cost $12 and child tickets cost $8. On a certain day, a total of 200 tickets were sold, and the total revenue was $2,160. If aa represents the number of adult tickets sold, which equation describes this situation?

  1. 12a+8(a−200)=216012a + 8(a - 200) = 2160
  2. 12a+8(200−a)=216012a + 8(200 - a) = 2160 (correct answer)
  3. 12a+8c=216012a + 8c = 2160
  4. 20(a)=216020(a) = 2160
Explanation: Let aa be the number of adult tickets. The revenue from adult tickets is 12a12a. Since a total of 200 tickets were sold, the number of child tickets is 200−a200 - a. The revenue from child tickets is 8(200−a)8(200 - a). The total revenue is the sum of these two amounts, leading to the equation 12a+8(200−a)=216012a + 8(200 - a) = 2160.
  • A incorrectly represents the number of child tickets as a−200a - 200, which would be negative.
  • C uses two variables, aa and cc, without using the given information to create an equation in a single variable.
  • D incorrectly averages the ticket prices (12+8=20) and multiplies by the number of adult tickets.

Question 11

A company finds that the cost, CC, to produce xx widgets is given by C=3000+4xC = 3000 + 4x. The company wants to sell the widgets so that their profit is exactly $5000 when they sell 200 widgets. If pp is the selling price per widget, which equation can be used to find pp?

  1. 200p−3000=5000200p - 3000 = 5000
  2. 200p+(3000+4(200))=5000200p + (3000 + 4(200)) = 5000
  3. 5000=3000+4(200p)5000 = 3000 + 4(200p)
  4. 200p−(3000+4(200))=5000200p - (3000 + 4(200)) = 5000 (correct answer)
Explanation: Profit is calculated as Total Revenue - Total Cost. The Total Revenue from selling 200 widgets at price pp is 200p200p. The Total Cost to produce 200 widgets is C=3000+4(200)C = 3000 + 4(200). Setting the profit equal to $5000 gives the equation: Profit = Revenue - Cost, so 5000=200p−(3000+4(200))5000 = 200p - (3000 + 4(200)), which is equivalent to choice A.
  • B incorrectly adds the cost to the revenue instead of subtracting it.
  • C incorrectly structures the cost and revenue relationship.
  • D ignores the variable cost component (4x4x) of the total cost.

Question 12

Two cars leave from the same city at the same time and travel in opposite directions. One car travels at an average speed of 55 miles per hour, and the other travels at an average speed of 65 miles per hour. Which equation can be used to find the time in hours, tt, it will take for the cars to be 480 miles apart?

  1. 65t−55t=48065t - 55t = 480
  2. 55t+65t=48055t + 65t = 480 (correct answer)
  3. (65)(55)t=480(65)(55)t = 480
  4. t/55+t/65=480t/55 + t/65 = 480
Explanation: When two objects travel in opposite directions, their relative speed is the sum of their individual speeds. The distance they are apart is this combined speed multiplied by time. The distance traveled by the first car is 55t55t and the distance by the second car is 65t65t. Since they are moving apart, the total distance between them is the sum of their individual distances: 55t+65t=48055t + 65t = 480.
  • A represents the distance between two cars traveling in the same direction, where one is faster than the other.
  • C incorrectly multiplies the speeds instead of adding them.
  • D relates time and speed incorrectly, as if adding rates, not distances.

Question 13

A salesperson earns a base salary of $1,200 per month plus a 5% commission on all sales exceeding $10,000. Last month, the salesperson's total sales were SS dollars, where S>10,000S > 10,000. Which equation represents the salesperson's total monthly earnings, EE?

  1. E=1200+0.05SE = 1200 + 0.05S
  2. E=1200+0.05(S−10000)E = 1200 + 0.05(S - 10000) (correct answer)
  3. E=1200+0.05(10000)+SE = 1200 + 0.05(10000) + S
  4. E=1200(0.05)+(S−10000)E = 1200(0.05) + (S - 10000)
Explanation: The salesperson's earnings consist of the base salary ($1,200) and the commission. The commission is calculated only on the portion of sales exceeding $10,000. This amount is S−10,000S - 10,000. The commission is 5% of this amount, which is 0.05(S−10,000)0.05(S - 10,000). Therefore, the total earnings are E=1200+0.05(S−10000)E = 1200 + 0.05(S - 10000).
  • A incorrectly applies the commission to the total sales amount, SS, rather than just the amount over $10,000.
  • C incorrectly calculates commission on the first $10,000 and then adds the total sales amount.
  • D incorrectly multiplies the base salary by the commission rate and adds the commissionable sales amount without the rate.

Question 14

The population of Town A is 12,000 and is growing by 400 people per year. The population of Town B is 18,000 and is decreasing by 200 people per year. Which equation can be used to find the number of years, yy, it will take for the populations of the two towns to be equal?

  1. 12000+400y=18000−200y12000 + 400y = 18000 - 200y (correct answer)
  2. 12000+400y=18000+200y12000 + 400y = 18000 + 200y
  3. 400y−200y=18000−12000400y - 200y = 18000 - 12000
  4. (12000+18000)=(400−200)y(12000+18000) = (400-200)y
Explanation: To find when the populations are equal, we must set their expressions equal to each other. Town A's population after yy years is its initial population plus the growth: 12000+400y12000 + 400y. Town B's population after yy years is its initial population minus the decrease: 18000−200y18000 - 200y. Setting them equal gives 12000+400y=18000−200y12000 + 400y = 18000 - 200y.
  • B incorrectly shows Town B's population growing instead of decreasing.
  • C is an incorrect rearrangement of the equation.
  • D incorrectly combines the initial populations and the rates of change.

Question 15

A library charges a fine for overdue books based on a fixed amount for the first day and a smaller, constant amount for each additional day. A book that is 4 days overdue has a fine of $1.75. A book that is 10 days overdue has a fine of $3.25. If dd represents the number of days a book is overdue (d≥1d \ge 1), which equation represents the fine, FF?

  1. F=0.25d+0.75F = 0.25d + 0.75
  2. F=1.75+0.25(d−4)F = 1.75 + 0.25(d - 4)
  3. F=0.25+1.00(d−1)F = 0.25 + 1.00(d - 1)
  4. F=1.00+0.25(d−1)F = 1.00 + 0.25(d - 1) (correct answer)
Explanation: Let the fine for the first day be f1f_1 and the fine for each additional day be aa. The total fine is F=f1+a(d−1)F = f_1 + a(d-1). From the given information, we have two equations: 1.75=f1+a(4−1)1.75 = f_1 + a(4-1) and 3.25=f1+a(10−1)3.25 = f_1 + a(10-1). Subtracting the first from the second gives 1.50=6a1.50 = 6a, so a=0.25a = 0.25. Substituting this back gives 1.75=f1+0.25(3)1.75 = f_1 + 0.25(3), so 1.75=f1+0.751.75 = f_1 + 0.75, which means f1=1.00f_1 = 1.00. The equation is F=1.00+0.25(d−1)F = 1.00 + 0.25(d - 1).
  • B correctly finds the additional day rate but uses one of the data points as the base fee, which is not the fee for day 1.
  • C swaps the first-day fee and the additional day rate.
  • D is a simplified form of choice A (F=1.00+0.25d−0.25=0.25d+0.75F = 1.00 + 0.25d - 0.25 = 0.25d + 0.75), but choice A more directly represents the structure described in the problem (a fee for the first day and a separate rate for additional days). Choice A is the better setup model.

Question 16

A manufacturing plant has a fixed daily cost of $5,000 and a variable cost of $15 for each unit produced. The company sells each unit for $40. Which equation could be used to determine the number of units, xx, that must be produced and sold in a day to break even (i.e., for total revenue to equal total cost)?

  1. 40x=5000+15x40x = 5000 + 15x (correct answer)
  2. 40x+15x=500040x + 15x = 5000
  3. x(40−15)=−5000x(40 - 15) = -5000
  4. 15x=5000+40x15x = 5000 + 40x
Explanation: The break-even point occurs when total revenue equals total cost. The total revenue from selling xx units is 40x40x. The total cost of producing xx units is the sum of the fixed cost and the variable cost, which is 5000+15x5000 + 15x. Setting these two expressions equal gives the break-even equation: 40x=5000+15x40x = 5000 + 15x.
  • B incorrectly adds the revenue and variable cost, rather than equating revenue with total cost.
  • C is a correct rearrangement of the equation to find profit, but sets it to a negative value. The question asks for the setup where revenue equals cost.
  • D incorrectly places the revenue on the cost side of the equation.

Question 17

A taxi service charges a flat fee of $3.50 plus an additional $2.25 for each mile traveled. A passenger has at most $44.00 to spend on the ride. If mm represents the number of miles traveled, which of the following equations represents the exact number of miles the passenger can travel to spend their entire budget?

  1. 2.25m+3.50=442.25m + 3.50 = 44 (correct answer)
  2. 3.50m+2.25=443.50m + 2.25 = 44
  3. (2.25+3.50)m=44(2.25 + 3.50)m = 44
  4. 2.25+3.50+m=442.25 + 3.50 + m = 44
Explanation: The total cost is the sum of the flat fee and the variable cost per mile. The flat fee is a constant $3.50. The variable cost is $2.25 multiplied by the number of miles, mm, which is (2.25m). Setting the sum of these two costs equal to the total budget of $44.00 gives the equation 2.25m+3.50=442.25m + 3.50 = 44.
  • B incorrectly multiplies the number of miles by the flat fee and adds the per-mile charge as a constant.
  • C incorrectly adds the fee and per-mile charge before multiplying by the number of miles, implying the flat fee is also charged for every mile.
  • D incorrectly adds all quantities together without multiplying the per-mile charge by the number of miles.

Question 18

The length of a rectangular garden is 5 feet less than twice its width. The perimeter of the garden is 80 feet. If ww represents the width of the garden, which equation can be used to find its width?

  1. w+(2w−5)=80w + (2w - 5) = 80
  2. w(2w−5)=80w(2w - 5) = 80
  3. 2w+2(2w−5)=802w + 2(2w - 5) = 80 (correct answer)
  4. 2w+(2w−10)=802w + (2w - 10) = 80
Explanation: The perimeter of a rectangle is given by the formula P=2L+2WP = 2L + 2W, where LL is the length and WW is the width. The problem states the width is ww and the length is 2w−52w - 5. Substituting these into the perimeter formula gives 80=2(2w−5)+2w80 = 2(2w - 5) + 2w. This is equivalent to 2w+2(2w−5)=802w + 2(2w - 5) = 80.
  • A incorrectly represents half the perimeter (one width plus one length).
  • B incorrectly sets the area of the garden, not the perimeter, equal to 80.
  • D incorrectly distributes the 2 only to the constant term in the expression for length, resulting in 2w+(2w−10)2w + (2w - 10) instead of 2(2w)−2(5)2(2w) - 2(5) which is 4w−104w - 10. The correct setup is 2w+4w−10=802w + 4w - 10 = 80. The choice represents half the perimeter.

Question 19

A rental car company charges a daily rate plus a fee per mile driven. The total cost for renting a car for one day and driving 120 miles is $89. The total cost for renting the same car for one day and driving 200 miles is $129. Which equation represents the total cost $CC fordrivingfor driving mm $ miles in one day?

  1. C=0.5m+29C = 0.5m + 29 (correct answer)
  2. C=0.5m+89C = 0.5m + 89
  3. C=29m+0.5C = 29m + 0.5
  4. C=1.6m−103C = 1.6m - 103
Explanation: Using points (120, 89) and (200, 129), the slope is (129-89)/(200-120) = 40/80 = 0.5. Using point (120, 89): C - 89 = 0.5(m - 120), so C = 0.5m + 29. Choice B incorrectly uses 89 as the y-intercept. Choice C switches the slope and y-intercept values. Choice D results from using an incorrect calculation method.

Question 20

A plant's height increases linearly with time. On day 10 after planting, the plant was 15 cm tall. On day 25 after planting, it was 27 cm tall. Which equation can be used to find the plant's height HH (in cm) on day dd after planting?

  1. H=0.8d+15H = 0.8d + 15
  2. H=1.25d−0.5H = 1.25d - 0.5
  3. H=0.8d+7H = 0.8d + 7 (correct answer)
  4. H=12d−105H = 12d - 105
Explanation: When you encounter a linear growth problem, you're working with a straight line relationship that can be expressed as H=md+bH = md + b, where mm is the slope (rate of change) and bb is the y-intercept. You have two data points: (10, 15) and (25, 27). First, find the slope using m=y2−y1x2−x1=27−1525−10=1215=0.8m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{27 - 15}{25 - 10} = \frac{12}{15} = 0.8 cm per day. This means the plant grows 0.8 cm each day. Now use the point-slope form with either data point. Using (10, 15): H=0.8d+bH = 0.8d + b, so 15=0.8(10)+b15 = 0.8(10) + b, which gives us 15=8+b15 = 8 + b, therefore b=7b = 7. The equation is H=0.8d+7H = 0.8d + 7. Let's check why the other answers are wrong. Answer A (H=0.8d+15H = 0.8d + 15) has the correct slope but treats the height on day 10 as the y-intercept, which would mean the plant was 15 cm tall on day 0. Answer B (H=1.25d−0.5H = 1.25d - 0.5) uses an incorrect slope of 1.25 instead of 0.8. Answer D (H=12d−105H = 12d - 105) uses the height difference (12 cm) as the slope instead of dividing by the time difference. Always verify your linear equation by plugging in both given points to ensure they produce the correct heights. This catches calculation errors and confirms you've identified the right relationship between the variables.