Algebra Flashcards: Creating And Graphing Two Variable Equations

What this deck covers

This deck focuses on Creating And Graphing Two Variable Equations, giving you a quick way to review the definitions, rules, and examples that matter most for Algebra.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What is the equation for a line with slope $-2$ and $y$-intercept $5$?

Answer: $y=-2x+5$. Substitute slope and $y$-intercept into $y=mx+b$.

Flashcard 2: What is the equation for the area $A$ of a circle with radius $r$?

Answer: $A=\pi r^2$. Space enclosed by the circle.

Flashcard 3: What is the equation for direct variation between $y$ and $x$ with constant $k$?

Answer: $y=kx$. Direct variation passes through the origin.

Flashcard 4: What is the equation in slope-intercept form for $-3x+6y=12$?

Answer: $y=\frac{1}{2}x+2$. Divide by $6$: $y=\frac{1}{2}x+2$.

Flashcard 5: What is the equation for cost $C$ if fixed cost is $50$ and variable cost is $6$ per unit $x$?

Answer: $C=6x+50$. Fixed cost plus variable cost per unit.

Flashcard 6: What is the equation for taxi cost $C$ with base fare $4$ and $2.5$ dollars per mile $m$?

Answer: $C=2.5m+4$. Base fare plus cost per mile.

Flashcard 7: What is the equation for the circumference $C$ of a circle with radius $r$?

Answer: $C=2\pi r$. Distance around the circle's edge.

Flashcard 8: Identify the equation modeling "$y$ varies directly with $x$" and $y=12$ when $x=3$.

Answer: $y=4x$. Find $k$: $12=k(3)$, so $k=4$.

Flashcard 9: What is the meaning of $b$ in $y=mx+b$ in terms of an initial value?

Answer: $b$ is the initial value when $x=0$. The $y$-intercept represents the starting value.

Flashcard 10: What is the equation for a constant difference relationship where $y$ is $7$ less than $x$?

Answer: $y=x-7$. Subtract $7$ from any $x$-value to get $y$.

Flashcard 11: What is the equation for distance $d$ traveled at constant speed $v$ for time $t$?

Answer: $d=vt$. Distance equals rate times time.

Flashcard 12: What is the equation for a line with slope $-2$ and $y$-intercept $5$?

Answer: $y=-2x+5$. Substitute slope and $y$-intercept into $y=mx+b$.

Flashcard 13: Which $x$-values are most efficient to graph $y=2x-1$ quickly by a table?

Answer: Use small integers such as $x=-1,0,1$. Easy values for mental calculation.

Flashcard 14: What is the equation for simple interest $I$ with principal $P$, rate $r$, and time $t$?

Answer: $I=Prt$. Interest equals principal times rate times time.

Flashcard 15: What scale choice is appropriate when graphing points with coordinates up to $20$?

Answer: Use a consistent scale such as $1$ or $2$ units per grid mark. Prevents crowding and ensures readability.

Flashcard 16: What is the equation of the line through $(2,-1)$ with slope $2$?

Answer: $y=2x-5$. Use point-slope form with $(2,-1)$ and $m=2$.

Flashcard 17: What is the $x$-intercept of a graph, stated as a condition on $y$?

Answer: The $x$-intercept occurs where $y=0$. Set $y=0$ and solve for $x$.

Flashcard 18: What is the equation of the line through $(2,-1)$ with slope $2$?

Answer: $y=2x-5$. Use point-slope form with $(2,-1)$ and $m=2$.

Flashcard 19: What is the equation of a vertical line passing through $x=3$?

Answer: $x=3$. Vertical lines have constant $x$-coordinate.

Flashcard 20: What is the equation for profit $P$ if revenue is $R$ and cost is $C$?

Answer: $P=R-C$. Revenue minus total costs.

Flashcard 21: Identify the equation modeling "$y$ varies directly with $x$" and $y=-10$ when $x=5$.

Answer: $y=-2x$. Find $k$: $-10=k(5)$, so $k=-2$.

Flashcard 22: Identify the equation modeling "$y$ varies directly with $x$" and $y=12$ when $x=3$.

Answer: $y=4x$. Find $k$: $12=k(3)$, so $k=4$.

Flashcard 23: What is the $y$-intercept of a line written in the form $y=mx+b$?

Answer: The $y$-intercept is $b$. The constant term gives the $y$-intercept.

Flashcard 24: Identify the independent variable in the model $C=3v+10$ where $v$ is number of visits.

Answer: The independent variable is $v$. The input variable that can be chosen.

Flashcard 25: What is the $y$-intercept of a graph, stated as a condition on $x$?

Answer: The $y$-intercept occurs where $x=0$. Set $x=0$ and solve for $y$.

Flashcard 26: What is the $y$-intercept of the line $3x+2y=8$?

Answer: $y=4$. Set $x=0$ in $3x+2y=8$ to get $y=4$.

Flashcard 27: Identify the dependent variable in the model $C=3v+10$ where $v$ is number of visits.

Answer: The dependent variable is $C$. The output variable that depends on $v$.

Flashcard 28: What is the $y$-intercept of a line written in the form $y=mx+b$?

Answer: The $y$-intercept is $b$. The constant term gives the $y$-intercept.

Flashcard 29: What is the equation for a constant difference relationship where $y$ is $5$ more than $x$?

Answer: $y=x+5$. Add $5$ to any $x$-value to get $y$.

Flashcard 30: What is the equation of a horizontal line passing through $y=-2$?

Answer: $y=-2$. Horizontal lines have constant $y$-coordinate.

Flashcard 31: What is the equation in slope-intercept form for $2x+y=7$?

Answer: $y=-2x+7$. Solve for $y$: $y=-2x+7$.

Flashcard 32: What is the meaning of the slope $m$ in $y=mx+b$ as a rate of change?

Answer: $m$ is the change in $y$ per $1$ unit change in $x$. Slope measures the rate of change.

Flashcard 33: What is the $x$-intercept of a graph, stated as a condition on $y$?

Answer: The $x$-intercept occurs where $y=0$. Set $y=0$ and solve for $x$.

Flashcard 34: What is the standard form of a linear equation in two variables used in Algebra $1$?

Answer: $Ax+By=C$. General linear form with integer coefficients.

Flashcard 35: What is the equation for revenue $R$ when each item costs $8$ dollars and $x$ items are sold?

Answer: $R=8x$. Price per item times number sold.

Flashcard 36: What is the equation for total pay $P$ with hourly wage $15$ and $h$ hours worked?

Answer: $P=15h$. Hourly wage times hours worked.

Flashcard 37: What does the variable $y$ typically represent on a coordinate plane when graphing an equation?

Answer: $y$ represents the dependent variable (vertical axis). It depends on the $x$-value chosen.

Flashcard 38: What is the meaning of the slope $m$ in $y=mx+b$ as a rate of change?

Answer: $m$ is the change in $y$ per $1$ unit change in $x$. Slope measures the rate of change.

Flashcard 39: What is the slope of the line through $(0,2)$ and $(3,11)$?

Answer: $m=3$. Use slope formula: $m=\frac{11-2}{3-0}=3$.

Flashcard 40: What is the equation for a line with slope $4$ and $y$-intercept $-3$?

Answer: $y=4x-3$. Substitute slope and $y$-intercept into $y=mx+b$.

Flashcard 41: What is the equation for a line with slope $4$ and $y$-intercept $-3$?

Answer: $y=4x-3$. Substitute slope and $y$-intercept into $y=mx+b$.

Flashcard 42: What is the equation for total distance $d$ if you start with $d_0$ and travel at speed $v$ for time $t$?

Answer: $d=d_0+vt$. Initial distance plus distance traveled.

Flashcard 43: What is the first step to graph an equation in two variables by making a table?

Answer: Choose $x$-values and compute the corresponding $y$-values. Create ordered pairs to plot.

Flashcard 44: What is the $x$-intercept of the line $3x+2y=8$?

Answer: $x=\frac{8}{3}$. Set $y=0$ in $3x+2y=8$ to get $x=\frac{8}{3}$.

Flashcard 45: Identify the equation for Celsius $C$ in terms of Fahrenheit $F$ using a linear conversion.

Answer: $C=\frac{5}{9}(F-32)$. Linear conversion from Fahrenheit to Celsius.

Flashcard 46: What is the equation for total cost $C$ with $10$ dollar membership fee plus $3$ dollars per visit $v$?

Answer: $C=3v+10$. Fixed fee plus cost per visit.

Flashcard 47: What is the slope-intercept form of a linear equation in two variables?

Answer: $y=mx+b$. Standard form with slope $m$ and $y$-intercept $b$.

Flashcard 48: Find the missing value: If $(2,y)$ is on $y=3x-4$, what is $y$?

Answer: $y=2$. Substitute $x=2$: $y=3(2)-4=2$.

Flashcard 49: Find the missing value: If $(2,y)$ is on $y=3x-4$, what is $y$?

Answer: $y=2$. Substitute $x=2$: $y=3(2)-4=2$.

Flashcard 50: What does it mean for an ordered pair $(x,y)$ to be a solution of an equation in two variables?

Answer: $(x,y)$ makes the equation true when substituted. The coordinates satisfy the equation exactly.

Flashcard 51: What is the equation for the area $A$ of a rectangle with length $L$ and width $W$?

Answer: $A=LW$. Product of length and width.

Flashcard 52: What is the slope of the line through $(2,5)$ and $(6,1)$?

Answer: $m=-1$. Use slope formula: $m=\frac{1-5}{6-2}=-1$.

Flashcard 53: Find the missing value: If $(x,5)$ is on $y=2x+1$, what is $x$?

Answer: $x=2$. Substitute $y=5$: $5=2x+1$, so $x=2$.

Flashcard 54: What labels should be included on a coordinate graph of $y$ versus $x$?

Answer: Label axes with variable names and units (if given). Proper labeling makes graphs interpretable.

Flashcard 55: What is the equation for the perimeter $P$ of a rectangle with length $L$ and width $W$?

Answer: $P=2L+2W$. Sum of all four sides of a rectangle.

Flashcard 56: What is the equation of the line through $(1,4)$ with slope $-3$?

Answer: $y=-3x+7$. Use point-slope form with $(1,4)$ and $m=-3$.

Flashcard 57: What is the slope formula between two points $(x_1,y_1)$ and $(x_2,y_2)$?

Answer: $m=\frac{y_2-y_1}{x_2-x_1}$. Change in $y$ divided by change in $x$.

Flashcard 58: What is the slope formula between two points $(x_1,y_1)$ and $(x_2,y_2)$?

Answer: $m=\frac{y_2-y_1}{x_2-x_1}$. Change in $y$ divided by change in $x$.

Flashcard 59: What is the equation for a proportional relationship between $y$ and $x$?

Answer: $y=kx$ for some constant $k$. The ratio $\frac{y}{x}$ remains constant.

Flashcard 60: What is the equation for total pay $P$ with hourly wage $15$ and $h$ hours worked?

Answer: $P=15h$. Hourly wage times hours worked.

Flashcard 61: Identify the equation for Fahrenheit $F$ in terms of Celsius $C$ using a linear conversion.

Answer: $F=\frac{9}{5}C+32$. Linear conversion from Celsius to Fahrenheit.

Flashcard 62: What does the variable $x$ typically represent on a coordinate plane when graphing an equation?

Answer: $x$ represents the independent variable (horizontal axis). It's the input value that can be chosen freely.

Flashcard 63: What is the equation for total amount $A$ after simple interest, using $A$, $P$, $r$, and $t$?

Answer: $A=P+Prt$. Principal plus interest earned.

Flashcard 64: What is the $x$-intercept of the line $3x+2y=8$?

Answer: $x=\frac{8}{3}$. Set $y=0$ in $3x+2y=8$ to get $x=\frac{8}{3}$.

Flashcard 65: What is the equation for total cost $C$ with a fixed fee $f$ and rate $r$ per unit $x$?

Answer: $C=rx+f$. Fixed fee plus variable cost per unit.

Flashcard 66: What is the equation for distance $d$ traveled at constant speed $v$ for time $t$?

Answer: $d=vt$. Distance equals rate times time.

Flashcard 67: Identify the slope and $y$-intercept in $y=-\frac{3}{4}x+6$.

Answer: $m=-\frac{3}{4}$ and $b=6$. Coefficient of $x$ is slope, constant is $y$-intercept.

Flashcard 68: What is the equation of the line through $(1,4)$ with slope $-3$?

Answer: $y=-3x+7$. Use point-slope form with $(1,4)$ and $m=-3$.

Flashcard 69: Identify the slope of the line given by $5x-10y=20$.

Answer: $m=\frac{1}{2}$. Rewrite as $y=\frac{1}{2}x-2$; slope is $\frac{1}{2}$.