This question tests your ability to create equations from real-world relationships and set up appropriate graphs to visualize them. When creating an equation from a context, first identify the two quantities that are related (like cost and number of items), choose variables to represent them (like C for cost and n for number), then write an equation that captures how one depends on the other. From the context, we have a rectangle with length x and width (x-4), and we need to find the area A. The area of a rectangle is length times width, so A = x × (x-4). This gives us A = x(x-4), which when expanded would be x² - 4x. This equation lets us calculate the area for any value of x greater than 4! Choice C is correct because it accurately represents the relationship using the area formula: length times width equals x times (x-4). Choice B creates a quadratic equation A = x² - 4, but this misses the multiplication: the area isn't x² minus 4, it's x times the quantity (x-4). When you see a product of two expressions, you need to multiply them together, not just subtract! Remember the difference between operations: when finding area of a rectangle, you multiply length times width. Here, that's x times (x-4), which gives x(x-4) or x² - 4x when expanded. Don't confuse this with simply subtracting 4 from x²!

This question tests your ability to create equations from real-world relationships and set up appropriate graphs to visualize them. When creating an equation from a context, first identify the two quantities that are related (like cost and hours), choose variables to represent them (like T for total cost and h for hours), then write an equation that captures how one depends on the other. From the context, cost is $12 fixed plus $4 per hour, we identify that T depends on h; the rate is 4 (that becomes our coefficient), and the starting amount is 12 (that's our constant term), so the equation is T = 4h + 12, which lets us calculate total cost for any hours rented! Choice C is correct because it accurately represents the relationship with the fixed fee as the constant and the hourly rate as the coefficient. Choice A has the numbers switched: it uses 12h + 4, but the context tells us $4 per hour (not $12) and $12 fixed (not $4); when translating words to equations, make sure each part corresponds to the description! Quick trick: the words in the problem often tell you what operation to use; 'per' or 'each' usually means multiply (like $4 per hour = 4 times hours), 'plus' means add (like plus $12 fee). After you create your equation, test it with simple values: try h = 0 (should give $12) and h = 1 (should give $16); if it matches, you've got it right!

This question tests your ability to create equations from real-world relationships and set up appropriate graphs to visualize them. When creating an equation from a context, first identify the two quantities that are related (like cost and number of items), choose variables to represent them (like C for cost and n for number), then write an equation that captures how one depends on the other. From the context, the runner moves at 6 miles per hour, we identify that distance d depends on time t. The rate is 6 miles per hour (that becomes our coefficient), and there's no starting distance mentioned (so no constant term). So the equation is d = 6t. This equation lets us calculate the distance traveled for any amount of time! Choice A is correct because it accurately represents the relationship with distance equal to 6 times the time, matching the constant speed of 6 miles per hour. Choice C has the variables switched: it says t = 6d, which would mean time equals 6 times the distance, but that would give us a speed of 1/6 miles per hour, not 6 miles per hour. When you see words like 'per,' that usually means multiplication in the direction stated! After you create your equation, test it with simple values: if d = 6t represents distance at 6 mph, try t = 1 (should give 6 miles) and t = 2 (should give 12 miles). If your equation gives the right outputs for these test inputs, you probably have it right!

This question tests your ability to create equations from real-world relationships and set up appropriate graphs to visualize them. When creating an equation from a context, first identify the two quantities that are related (like cost and number of items), choose variables to represent them (like C for cost and n for number), then write an equation that captures how one depends on the other. From the context, the theater charges $9 per ticket plus a $4 booking fee, we identify that total cost C depends on number of tickets t. The rate is $9 per ticket (that becomes our coefficient), and the booking fee is $4 (that's our constant term). So the equation is C = 9t + 4. This equation lets us calculate the total cost for any number of tickets! Choice C is correct because it accurately represents the relationship with $9 per ticket (9t) plus the $4 booking fee (+4). Choice A has the numbers switched: it puts $4 per ticket and a $9 fee, but the context tells us it's $9 per ticket and a $4 fee. When translating words to equations, make sure each part of the equation corresponds to something in the description! Quick trick: the words in the problem often tell you what operation to use. 'Per' or 'each' usually means multiply (like $9 per ticket = 9 times number of tickets). 'Plus' or 'and' means add (like $4 fee plus ticket cost). Listen to the language!

This question tests your ability to create equations from real-world relationships and set up appropriate graphs to visualize them. The coordinate plane helps us visualize relationships: the horizontal x-axis typically shows the independent variable (the one you choose or that changes first, like time or quantity), while the vertical y-axis shows the dependent variable (the one that responds, like cost or height). For this relationship, the x-axis should represent months with label 'Months', and the y-axis should represent total cost with label 'Total Cost ($)', which makes sense because months is the independent variable (you choose how many months) and cost depends on that choice. Choice B is correct because it sets up the axes appropriately with months on x and cost on y, including the dollar units for cost. Choice A has the variables switched: it puts total cost on the x-axis and months on the y-axis, but remember—the independent variable (the one you start with or control) goes on the x-axis, and the dependent variable (the one that responds) goes on the y-axis. Remember the difference between independent and dependent variables: the independent variable is the one you can choose or control (like how many months you subscribe), and the dependent variable is the one that responds to your choice (like what the total cost is)—independent goes on the x-axis, dependent on the y-axis—this is the standard convention! For graphing, think about your audience: good axis labels include the variable name AND units (like 'Total Cost ($)' not just 'C'), and a good scale shows your data without bunching it up or spreading it too thin.

This question tests your ability to create equations from real-world relationships and set up appropriate graphs to visualize them. When creating an equation from a context, first identify the two quantities that are related (like length and width), choose variables to represent them (like l for length and w for width), then write an equation that captures how one depends on the other. From the context, perimeter is 40 feet which means twice length plus twice width equals 40, so the equation is 2l + 2w = 40; this lets us find possible widths for any length (or vice versa) to maintain the perimeter! Choice B is correct because it accurately represents the relationship with the sum of twice each dimension equaling the perimeter. Choice A has the wrong operation: it uses lw = 40 which is area, but the context says perimeter which means addition of sides; when you see 'perimeter,' think sum of sides! Quick trick: words like 'perimeter' mean add up the sides (2l + 2w), while 'area' means multiply (l * w); listen to the language! When creating equations, test with values: if l=10, then 2*10 + 2w=40 so w=10 (square garden); if it makes sense, you're on track!

This question tests your ability to create equations from real-world relationships and set up appropriate graphs to visualize them. When creating an equation from a context, first identify the two quantities that are related (like cost and number of items), choose variables to represent them (like C for cost and n for number), then write an equation that captures how one depends on the other. From the context, bracelets cost $5 each plus a one-time $10 setup fee, so the total cost C depends on the number of bracelets b. The rate is $5 per bracelet (that becomes our coefficient), and the starting amount is $10 (that's our constant term). So the equation is C = 5b + 10. This equation lets us calculate the total cost for any number of bracelets! Choice C is correct because it accurately represents the relationship with $5 per bracelet (5b) plus the $10 setup fee. Choice A has the numbers switched: it puts $10 per bracelet and a $5 fee, but the problem clearly states $5 is per bracelet and $10 is the setup fee. When translating words to equations, make sure each part of the equation corresponds to something in the description! Quick trick: the words in the problem often tell you what operation to use. 'Per' or 'each' usually means multiply (like $5 per bracelet = 5 times number of bracelets). 'Plus' or 'and' means add (like $10 fee plus bracelet cost). Listen to the language!

This question tests your ability to create equations from real-world relationships and set up appropriate graphs to visualize them. When creating an equation from a context, first identify the two quantities that are related (like cost and number of items), choose variables to represent them (like C for cost and n for number), then write an equation that captures how one depends on the other. From the context, a rectangle's perimeter is the distance around it, we identify that perimeter depends on both length l and width w. The perimeter formula is P = 2l + 2w (two lengths plus two widths), and we're told P = 40. So the equation is 2l + 2w = 40. This equation lets us find valid length-width combinations! Choice B is correct because it accurately represents the perimeter relationship 2l + 2w = 40. Choice A creates an equation lw = 40, but that would be the area formula (length times width), not perimeter. When you see 'perimeter,' that means the distance around, which requires adding all sides! When creating equations from word problems, ask yourself: What formula applies here? Perimeter of a rectangle is 2l + 2w (add all four sides), while area is l × w (multiply dimensions). Don't mix them up!

This question tests your ability to create equations from real-world relationships and set up appropriate graphs to visualize them. The coordinate plane helps us visualize relationships: the horizontal x-axis typically shows the independent variable (the one you choose or that changes first, like time or quantity), while the vertical y-axis shows the dependent variable (the one that responds, like cost or height). For this relationship, the x-axis should represent Number of Games with that label, and the y-axis should represent Total Cost ($) with that label. This makes sense because you choose how many games to buy (independent), and the cost depends on that choice (dependent). Choice B is correct because it sets up the axes appropriately with the independent variable (number of games) on the x-axis and the dependent variable (total cost) on the y-axis, including proper units. Choice A has the variables switched: it puts Total Cost on the x-axis and Number of Games on the y-axis, but remember—the independent variable (the one you start with or control) goes on the x-axis, and the dependent variable (the one that responds) goes on the y-axis. Remember the difference between independent and dependent variables: the independent variable is the one you can choose or control (like how many items you buy), and the dependent variable is the one that responds to your choice (like what the total cost is). Independent goes on the x-axis, dependent on the y-axis—this is the standard convention!

This question tests your ability to create equations from real-world relationships and set up appropriate graphs to visualize them. When creating an equation from a context, first identify the two quantities that are related (like cost and number of items), choose variables to represent them (like C for cost and n for number), then write an equation that captures how one depends on the other. From the context, the bike rental charges $12 to rent (a fixed fee) plus $4 per hour, so the total cost C depends on the number of hours h. The rate is $4 per hour (that becomes our coefficient), and the starting amount is $12 (that's our constant term). So the equation is C = 4h + 12. This equation lets us calculate the total cost for any rental duration! Choice B is correct because it accurately represents the relationship with $4 per hour (4h) plus the $12 rental fee. Choice A has the numbers switched: it puts $12 per hour and a $4 fee, but the problem clearly states $12 is the rental fee and $4 is per hour. When translating words to equations, make sure each part of the equation corresponds to something in the description! After you create your equation, test it with simple values: if C = 4h + 12 represents cost for h hours, try h = 0 (should give the $12 fee) and h = 1 (should give $16). If your equation gives the right outputs for these test inputs, you probably have it right!