SAT Math Flashcards: Equations With Two Variables

What this deck covers

This deck focuses on Equations With Two Variables, giving you a quick way to review the definitions, rules, and examples that matter most for SAT Math.

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 general form of a linear equation in two variables?

Answer: $Ax + By = C$. Standard form where A, B, and C are constants.

Flashcard 2: Convert the point-slope equation $y - 2 = 3(x + 1)$ to standard form.

Answer: $3x - y = -5$. Expand and rearrange to $Ax + By = C$ form.

Flashcard 3: Find the y-intercept of the equation $2x + 3y = 6$.

Answer: $(0, 2)$. Set $x = 0$: $3y = 6$, so $y = 2$.

Flashcard 4: What is the slope of the line $y = -5x + 2$?

Answer: $-5$. Coefficient of $x$ in slope-intercept form.

Flashcard 5: Convert the equation $2x + 3y = 6$ to slope-intercept form.

Answer: $y = -\frac{2}{3}x + 2$. Isolate $y$ by subtracting $2x$ and dividing by $3$.

Flashcard 6: What is the formula for converting point-slope form to slope-intercept form?

Answer: $y - y_1 = m(x - x_1)$ to $y = mx + b$. Expand point-slope and solve for $y$.

Flashcard 7: Find the equation of the line with undefined slope through $(4, -1)$.

Answer: $x = 4$. Undefined slope means vertical line.

Flashcard 8: Find the slope of the line $y = -\frac{3}{2}x + 4$.

Answer: $-\frac{3}{2}$. Coefficient of $x$ in slope-intercept form.

Flashcard 9: Which form is $y = mx + b$ called?

Answer: Slope-intercept form. Shows slope $m$ and y-intercept $b$ directly.

Flashcard 10: What is the slope of the line $y = -5x + 2$?

Answer: $-5$. Coefficient of $x$ in slope-intercept form.

Flashcard 11: What is the x-coordinate of the point where the line $y = 2x + 3$ crosses the x-axis?

Answer: $-\frac{3}{2}$. Set $y = 0$: $0 = 2x + 3$, so $x = -\frac{3}{2}$.

Flashcard 12: What is the slope of a line parallel to $y = \frac{1}{2}x - 3$?

Answer: $\frac{1}{2}$. Parallel lines have identical slopes.

Flashcard 13: What is the standard form of a linear equation in two variables?

Answer: $Ax + By = C$. General form with integer coefficients $A$, $B$, and $C$.

Flashcard 14: Find the x-intercept of the line $3x + 4y = 12$.

Answer: The x-intercept is $x = 4$.. Set $y = 0$ and solve for $x$.

Flashcard 15: Identify the slope in the equation $y = 3x + 7$. What is it?

Answer:

1. In $y = mx + b$ form, the coefficient of $x$ is the slope.

Flashcard 16: What is the point-slope form of a line through $(x_1, y_1)$ with slope $m$?

Answer: $y - y_1 = m(x - x_1)$. Uses a known point and slope to define the line.

Flashcard 17: What is the slope of the line that is horizontal?

Answer:

1. Horizontal lines have zero rise over run.

Flashcard 18: What is the slope of the line $y = -3$?

Answer:

1. Horizontal lines have zero slope.

Flashcard 19: What is the slope of the line that is horizontal?

Answer:

1. Horizontal lines have zero rise over run.

Flashcard 20: What is the equation of a vertical line passing through $(5, -2)$?

Answer: $x = 5$. Vertical lines have constant $x$-values.

Flashcard 21: What is the slope of the line that is vertical?

Answer: Undefined. Vertical lines have no finite slope.

Flashcard 22: Convert the equation $2x + 3y = 6$ to slope-intercept form.

Answer: $y = -\frac{2}{3}x + 2$. Isolate $y$ by subtracting $2x$ and dividing by $3$.

Flashcard 23: What is the formula for the slope of a line given points $(x_1, y_1)$ and $(x_2, y_2)$?

Answer: Slope $m = \frac{y_2 - y_1}{x_2 - x_1}$. Rise over run between two points.

Flashcard 24: Find the x-intercept of the line $3x + 4y = 12$.

Answer: The x-intercept is $x = 4$.. Set $y = 0$ and solve for $x$.

Flashcard 25: What is the equation of a horizontal line passing through $(3, 7)$?

Answer: $y = 7$. Horizontal lines have constant $y$-values.

Flashcard 26: Find the y-intercept of the line $3x + 6y = 12$.

Answer: $(0, 2)$. Set $x = 0$: $6y = 12$, so $y = 2$.

Flashcard 27: What is the equation of a horizontal line passing through $(3, 7)$?

Answer: $y = 7$. Horizontal lines have constant $y$-values.

Flashcard 28: Solve for $y$: $4x - 2y = 8$.

Answer: $y = 2x - 4$. Isolate $y$ by subtracting $4x$ and dividing by $-2$.

Flashcard 29: What is the y-intercept in the equation $y = mx + b$?

Answer: $b$. Constant term where line crosses y-axis.

Flashcard 30: What is the standard form of a linear equation with two variables?

Answer: $Ax + By = C$. General linear form where $A$, $B$, and $C$ are constants.

Flashcard 31: Convert $y = -2x + 5$ to standard form.

Answer: $2x + y = 5$. Move $x$-term to left: $2x + y = 5$.

Flashcard 32: Find the x-intercept of the equation $3x + 2y = 12$. What is it?

Answer: $x = 4$. Set $y = 0$ and solve for $x$.

Flashcard 33: What is the slope of the line $y = -3$?

Answer:

1. Horizontal lines have zero slope.

Flashcard 34: Find the equation of a line with slope $0$ through $(-2, 5)$.

Answer: $y = 5$. Zero slope creates horizontal line.

Flashcard 35: What is the standard form of a linear equation in two variables?

Answer: $Ax + By = C$. General form with integer coefficients $A$, $B$, and $C$.

Flashcard 36: Find the equation of a line with slope $3$ and y-intercept $-4$.

Answer: $y = 3x - 4$. Direct substitution into $y = mx + b$ form.

Flashcard 37: What is the slope of a line perpendicular to $y = 4x + 7$?

Answer: $-\frac{1}{4}$. Perpendicular slopes are negative reciprocals.

Flashcard 38: What is the formula for converting point-slope form to slope-intercept form?

Answer: $y - y_1 = m(x - x_1)$ to $y = mx + b$. Expand point-slope and solve for $y$.

Flashcard 39: Find the x-intercept of the line $y = 4x - 8$.

Answer: $(2, 0)$. Set $y = 0$: $0 = 4x - 8$, so $x = 2$.

Flashcard 40: What is the y-coordinate of the point where the line $2x + 5y = 10$ crosses the y-axis?

Answer: $2$. Set $x = 0$: $5y = 10$, so $y = 2$.

Flashcard 41: What is the general form of a linear equation in two variables?

Answer: $Ax + By = C$. Standard form where A, B, and C are constants.

Flashcard 42: Find the x-intercept of the equation $4x - y = 8$.

Answer: $(2, 0)$. Set $y = 0$: $4x = 8$, so $x = 2$.

Flashcard 43: Convert $y = 3x - 2$ to point-slope form through $(1, 1)$.

Answer: $y - 1 = 3(x - 1)$. Use point $(1,1)$ in point-slope formula.

Flashcard 44: What is the y-coordinate of the point where the line $2x + 5y = 10$ crosses the y-axis?

Answer: $2$. Set $x = 0$: $5y = 10$, so $y = 2$.

Flashcard 45: Find the x-intercept of the equation $3x + 2y = 12$. What is it?

Answer: $x = 4$. Set $y = 0$ and solve for $x$.

Flashcard 46: What is the formula for a line in point-slope form?

Answer: $y - y_1 = m(x - x_1)$. Uses known point $(x_1, y_1)$ and slope $m$.

Flashcard 47: Find the y-intercept of the line $3x + 6y = 12$.

Answer: $(0, 2)$. Set $x = 0$: $6y = 12$, so $y = 2$.

Flashcard 48: Determine the slope of the line $y = -5x + 3$.

Answer: The slope is $-5$. The coefficient of $x$ in slope-intercept form.

Flashcard 49: Solve for $y$: $4x - 2y = 8$.

Answer: $y = 2x - 4$. Divide both sides by -2 to isolate $y$.

Flashcard 50: What is the slope of the line $x = 7$?

Answer: Undefined. Vertical lines have undefined slope.

Flashcard 51: What is the slope of the line $x = 7$?

Answer: Undefined. Vertical lines have undefined slope.

Flashcard 52: Convert the equation $2x + 3y = 6$ to slope-intercept form.

Answer: $y = -\frac{2}{3}x + 2$. Solve for $y$ by isolating it on one side.

Flashcard 53: Find the slope of the line $y = -\frac{3}{2}x + 4$.

Answer: $-\frac{3}{2}$. Coefficient of $x$ in slope-intercept form.

Flashcard 54: Solve for $y$: $4x - 2y = 8$.

Answer: $y = 2x - 4$. Isolate $y$ by subtracting $4x$ and dividing by $-2$.

Flashcard 55: Find the equation of a line with slope $3$ and y-intercept $-4$.

Answer: $y = 3x - 4$. Direct substitution into $y = mx + b$ form.

Flashcard 56: What is the slope of a line perpendicular to $y = 4x + 7$?

Answer: $-\frac{1}{4}$. Perpendicular slopes are negative reciprocals.

Flashcard 57: Find the equation of a line perpendicular to $y = 2x + 1$ through $(3, 2)$.

Answer: $y = -\frac{1}{2}x + \frac{7}{2}$. Perpendicular slope $-\frac{1}{2}$, use point-slope form.

Flashcard 58: Find the equation of a line parallel to $y = -\frac{1}{3}x + 2$ through $(6, 4)$.

Answer: $y = -\frac{1}{3}x + 6$. Same slope, different y-intercept through given point.

Flashcard 59: What is the formula for a line in point-slope form?

Answer: $y - y_1 = m(x - x_1)$. Uses known point $(x_1, y_1)$ and slope $m$.

Flashcard 60: Identify the slope in the equation $y = mx + b$.

Answer: $m$. Coefficient of $x$ represents the rate of change.

Flashcard 61: Find the slope of the line given by $2x - 3y = 6$.

Answer: $\frac{2}{3}$. Rearrange to $y = \frac{2}{3}x - 2$ to identify slope.

Flashcard 62: State the condition for two lines to be parallel.

Answer: Slopes are equal. Parallel lines have identical slopes but different intercepts.

Flashcard 63: Find the slope of the line passing through $(2, 3)$ and $(4, 7)$.

Answer: $2$. Use slope formula: $\frac{7-3}{4-2} = \frac{4}{2} = 2$.

Flashcard 64: Identify the slope in the equation $y = mx + b$.

Answer: $m$. Coefficient of $x$ represents the rate of change.

Flashcard 65: What is the y-intercept of the equation $y = -4x + 9$?

Answer:

1. In $y = mx + b$ form, $b$ is the y-intercept.

Flashcard 66: What is the equation of a vertical line passing through $(5, -2)$?

Answer: $x = 5$. Vertical lines have constant $x$-values.

Flashcard 67: State the formula for the slope between points $(x_1, y_1)$ and $(x_2, y_2)$.

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

Flashcard 68: Convert the equation $3x + 4y = 12$ to slope-intercept form.

Answer: $y = -\frac{3}{4}x + 3$. Solve for $y$: $4y = -3x + 12$, then $y = -\frac{3}{4}x + 3$.

Flashcard 69: Find the x-intercept of the line $y = 4x - 8$.

Answer: $(2, 0)$. Set $y = 0$: $0 = 4x - 8$, so $x = 2$.

Flashcard 70: What is the slope of the line that is vertical?

Answer: Undefined. Vertical lines have no finite slope.

Flashcard 71: State the formula for the slope of a line between points $(x_1, y_1)$ and $(x_2, y_2)$.

Answer: $m = \frac{y_2 - y_1}{x_2 - x_1}$. Rise over run formula for any two points.

Flashcard 72: What is the value of $x$ in the system: $2x + 3y = 6$, $x - y = 1$?

Answer: $x = 3$. Substitute and solve the system of equations.

Flashcard 73: Identify the y-intercept in the equation $y = mx + b$.

Answer: The y-intercept is $b$. The constant term where the line crosses the y-axis.

Flashcard 74: What is the x-coordinate of the point where the line $y = 2x + 3$ crosses the x-axis?

Answer: $-\frac{3}{2}$. Set $y = 0$: $0 = 2x + 3$, so $x = -\frac{3}{2}$.

Flashcard 75: Find the equation of the line with undefined slope through $(4, -1)$.

Answer: $x = 4$. Undefined slope means vertical line.

Flashcard 76: Find the solution for $x$ if $y = 3$ in the equation $2x + y = 7$.

Answer: $x = 2$. Substitute $y = 3$ and solve: $2x + 3 = 7$.

Flashcard 77: Convert the equation $3x + 4y = 12$ to slope-intercept form.

Answer: $y = -\frac{3}{4}x + 3$. Solve for $y$: $4y = -3x + 12$, then $y = -\frac{3}{4}x + 3$.

Flashcard 78: Convert $y = 3x - 2$ to point-slope form through $(1, 1)$.

Answer: $y - 1 = 3(x - 1)$. Use point $(1,1)$ in point-slope formula.

Flashcard 79: Find the equation of the line with slope $-2$ passing through $(1, 4)$.

Answer: $y = -2x + 6$. Use point-slope: $y - 4 = -2(x - 1)$, then solve.

Flashcard 80: Does the equation $y = 2x + 3$ represent a function? Yes or No.

Answer: Yes. Each x-value has exactly one y-value.

Flashcard 81: State the condition for two lines to be parallel.

Answer: Slopes are equal. Parallel lines have identical slopes but different intercepts.

Flashcard 82: What is the point-slope form of a line through $(x_1, y_1)$ with slope $m$?

Answer: $y - y_1 = m(x - x_1)$. Uses a known point and slope to define the line.

Flashcard 83: What form is the equation $y - 3 = 2(x - 1)$ in?

Answer: Point-slope form. Form $y - y_1 = m(x - x_1)$ with known point.

Flashcard 84: Find the solution for $x$ if $y = 3$ in the equation $2x + y = 7$.

Answer: $x = 2$. Substitute $y = 3$ and solve: $2x + 3 = 7$.

Flashcard 85: What is the y-intercept in the equation $y = mx + b$?

Answer: $b$. Constant term where line crosses y-axis.

Flashcard 86: Convert the point-slope equation $y - 2 = 3(x + 1)$ to standard form.

Answer: $3x - y = -5$. Expand and rearrange to $Ax + By = C$ form.

Flashcard 87: Find the equation of a line with slope $0$ through $(-2, 5)$.

Answer: $y = 5$. Zero slope creates horizontal line.

Flashcard 88: Find the equation of the line with slope $-2$ passing through $(1, 4)$.

Answer: $y = -2x + 6$. Use point-slope: $y - 4 = -2(x - 1)$, then solve.

Flashcard 89: Convert the equation $2x + 3y = 6$ to slope-intercept form.

Answer: $y = -\frac{2}{3}x + 2$. Solve for $y$ by isolating it on one side.

Flashcard 90: What is the standard form of a linear equation with two variables?

Answer: $Ax + By = C$. General linear form where $A$, $B$, and $C$ are constants.

Flashcard 91: Find the equation of a line perpendicular to $y = 2x + 1$ through $(3, 2)$.

Answer: $y = -\frac{1}{2}x + \frac{7}{2}$. Perpendicular slope $-\frac{1}{2}$, use point-slope form.

Flashcard 92: What is the formula for the slope of a line given points $(x_1, y_1)$ and $(x_2, y_2)$?

Answer: Slope $m = \frac{y_2 - y_1}{x_2 - x_1}$. Rise over run between two points.

Flashcard 93: Find the x-intercept of the equation $4x - y = 8$.

Answer: $(2, 0)$. Set $y = 0$: $4x = 8$, so $x = 2$.

Flashcard 94: What form is the equation $y - 3 = 2(x - 1)$ in?

Answer: Point-slope form. Form $y - y_1 = m(x - x_1)$ with known point.

Flashcard 95: What is the slope of a line parallel to $y = \frac{1}{2}x - 3$?

Answer: $\frac{1}{2}$. Parallel lines have identical slopes.

Flashcard 96: Does the equation $y = 2x + 3$ represent a function? Yes or No.

Answer: Yes. Each x-value has exactly one y-value.

Flashcard 97: Identify the form of $2x + 3y = 6$.

Answer: Standard form. Form $Ax + By = C$ with integer coefficients.

Flashcard 98: Identify the form of $2x + 3y = 6$.

Answer: Standard form. Form $Ax + By = C$ with integer coefficients.

Flashcard 99: Identify the slope in the equation $y = 3x + 7$. What is it?

Answer:

1. In $y = mx + b$ form, the coefficient of $x$ is the slope.

Flashcard 100: Find the y-intercept of the equation $2x + 3y = 6$.

Answer: $(0, 2)$. Set $x = 0$: $3y = 6$, so $y = 2$.