SAT Math Flashcards: Graphs

What this deck covers

This deck focuses on Graphs, 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 slope-intercept form of a linear equation?

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

Flashcard 2: What is the general form of the equation of a parabola?

Answer: $y = ax^2 + bx + c$. Quadratic with degree 2 polynomial.

Flashcard 3: What is the equation for a line perpendicular to $y = -\frac{1}{4}x + 2$ at $(0, 0)$?

Answer: $y = 4x$. Negative reciprocal slope through given point.

Flashcard 4: Determine the x-intercept of the line $y = 2x - 8$.

Answer:

1. Set $y = 0$ and solve: $0 = 2x - 8$, so $x = 4$.

Flashcard 5: What is the slope formula for a line passing through points $(x_1, y_1)$ and $(x_2, y_2)$?

Answer: $m = \frac{y_2 - y_1}{x_2 - x_1}$. Change in $y$ over change in $x$ between two points.

Flashcard 6: Identify the slope of the line $y - 6 = \frac{1}{3}(x - 3)$.

Answer: $\frac{1}{3}$. Coefficient of $(x - 3)$ in point-slope form.

Flashcard 7: What is the equation of a vertical line through point $(a, b)$?

Answer: $x = a$. All points have the same $x$-coordinate.

Flashcard 8: Identify whether the line $x = 5$ is vertical or horizontal.

Answer: Vertical. Constant $x$-value creates vertical line.

Flashcard 9: Identify the direction of opening for the parabola $y = -x^2 + 4x - 1$.

Answer: Downward. Negative coefficient of $x^2$ opens downward.

Flashcard 10: What type of graph represents the equation $y = x^2$?

Answer: Parabola. Quadratic function creates U-shaped curve.

Flashcard 11: What is the equation of a circle with center $(h, k)$ and radius $r$?

Answer: $(x - h)^2 + (y - k)^2 = r^2$. Distance from center to any point on circle.

Flashcard 12: What is the slope of a line with equation $y = 0$?

Answer:

1. Horizontal line has zero rise over run.

Flashcard 13: Which form of a line's equation uses the formula $y - y_1 = m(x - x_1)$?

Answer: Point-slope form. Uses a known point $(x_1, y_1)$ and slope $m$.

Flashcard 14: Identify the vertex of the parabola $y = (x - 2)^2 - 3$.

Answer: $(2, -3)$. Vertex form shows $(h, k)$ as the turning point.

Flashcard 15: Identify the y-intercept in the equation $y = 3x + 4$.

Answer:

1. The constant term when $x = 0$.

Flashcard 16: What are the intercepts in the equation $y = \frac{1}{2}x - 3$?

Answer: x-intercept: 6, y-intercept: -3. Set each variable to zero alternately.

Flashcard 17: Determine the x-intercept of the line $y = 2x - 8$.

Answer:

1. Set $y = 0$ and solve: $0 = 2x - 8$, so $x = 4$.

Flashcard 18: What is the equation of a horizontal line through point $(a, b)$?

Answer: $y = b$. All points have the same $y$-coordinate.

Flashcard 19: Identify the x-intercept in the equation $2x - 6 = 0$.

Answer:

1. Solve for $x$ when $y = 0$.

Flashcard 20: State the vertex form of a quadratic function.

Answer: $y = a(x - h)^2 + k$. Shows vertex $(h, k)$ and vertical shift $k$.

Flashcard 21: What is the general form of a quadratic function?

Answer: $ax^2 + bx + c = 0$. Standard form with highest power of 2.

Flashcard 22: What is the slope formula for a line passing through points $(x_1, y_1)$ and $(x_2, y_2)$?

Answer: $m = \frac{y_2 - y_1}{x_2 - x_1}$. Change in $y$ over change in $x$ between two points.

Flashcard 23: Identify the slope in the equation $y = -5x + 2$.

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

Flashcard 24: What is the definition of a function in terms of ordered pairs?

Answer: Each input has exactly one output. Vertical line test ensures unique outputs.

Flashcard 25: What is the slope of a line with equation $y = 0$?

Answer:

1. Horizontal line has zero rise over run.

Flashcard 26: Identify the intercepts of the quadratic $y = (x - 3)(x + 2)$.

Answer: x-intercepts: $3, -2$. Set $y = 0$ to find where parabola crosses $x$-axis.

Flashcard 27: What is the equation of a circle with center $(h, k)$ and radius $r$?

Answer: $(x - h)^2 + (y - k)^2 = r^2$. Distance from center to any point on circle equals radius.

Flashcard 28: What are the coordinates of the y-intercept in the line $3x + 4y = 8$?

Answer: $(0, 2)$. Set $x = 0$ and solve for $y$.

Flashcard 29: Identify the slope of the line $y - 6 = \frac{1}{3}(x - 3)$.

Answer: $\frac{1}{3}$. Coefficient of $(x - 3)$ in point-slope form.

Flashcard 30: Identify the vertex of the parabola $y = (x - 2)^2 - 3$.

Answer: $(2, -3)$. Vertex form shows $(h, k)$ as the turning point.

Flashcard 31: Identify the direction of opening for the parabola $y = -x^2 + 4x - 1$.

Answer: Downward. Negative coefficient of $x^2$ opens downward.

Flashcard 32: Identify the slope of the line: $3x - 4y = 12$.

Answer: $\frac{3}{4}$. Rearrange to $y = \frac{3}{4}x - 3$ to identify slope.

Flashcard 33: What is the slope-intercept form of a linear equation?

Answer: $y = mx + b$. Shows slope $m$ and $y$-intercept $b$ directly.

Flashcard 34: What is the general form of the equation of a circle?

Answer: $x^2 + y^2 + Dx + Ey + F = 0$. Expanded form of circle equation.

Flashcard 35: Identify the transformation applied: $y = (x - 1)^2 + 2$.

Answer: Right 1 unit, up 2 units. Vertex form shows horizontal and vertical shifts.

Flashcard 36: What is the standard form of a linear equation?

Answer: $Ax + By = C$. Linear equation with integer coefficients and no fractions.

Flashcard 37: What is the equation of a line in slope-intercept form?

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

Flashcard 38: State the vertex form of a quadratic function.

Answer: $y = a(x - h)^2 + k$. Shows vertex $(h, k)$ and vertical shift $k$.

Flashcard 39: Identify the x-intercept in the equation $2x - 6 = 0$.

Answer:

1. Solve for $x$ when $y = 0$.

Flashcard 40: What is the radius of the circle $x^2 + y^2 = 16$?

Answer: $4$. Square root of the constant term.

Flashcard 41: What is the axis of symmetry for the parabola $y = ax^2 + bx + c$?

Answer: $x = -\frac{b}{2a}$. Vertical line through the vertex of the parabola.

Flashcard 42: Identify the center of the circle $(x - 3)^2 + (y + 4)^2 = 25$.

Answer: $(3, -4)$. Values of $(h, k)$ from standard form.

Flashcard 43: What is the vertex of the parabola $y = 3(x + 2)^2 - 5$?

Answer: $(-2, -5)$. Vertex form identifies $(h, k)$ directly.

Flashcard 44: What is the midpoint formula for the segment connecting $(x_1, y_1)$ and $(x_2, y_2)$?

Answer: $\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$. Average of the coordinates of the endpoints.

Flashcard 45: What is the standard form of a linear equation?

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

Flashcard 46: What is the slope-intercept form of a linear equation?

Answer: $y = mx + b$. Shows slope $m$ and $y$-intercept $b$ directly.

Flashcard 47: What is the equation for a line perpendicular to $y = -\frac{1}{4}x + 2$ at $(0, 0)$?

Answer: $y = 4x$. Negative reciprocal slope through given point.

Flashcard 48: What is the radius of the circle $x^2 + y^2 = 16$?

Answer:

1. Square root of the constant term.

Flashcard 49: What is the standard form of a linear equation?

Answer: $Ax + By = C$. Linear equation with integer coefficients and no fractions.

Flashcard 50: What is the equation for a line parallel to $y = 3x - 2$ passing through $(1, 4)$?

Answer: $y = 3x + 1$. Same slope, substitute point to find $b$.

Flashcard 51: Find the y-intercept of the line: $4x + 5y = 20$.

Answer:

1. Set $x = 0$: $5y = 20$, so $y = 4$.

Flashcard 52: What is the slope of a line perpendicular to $y = 2x + 3$?

Answer: $-\frac{1}{2}$. Negative reciprocal of the original slope.

Flashcard 53: What is the formula for converting a line from standard to slope-intercept form?

Answer: Solve $Ax + By = C$ for $y$. Isolate $y$ by dividing by coefficient of $y$.

Flashcard 54: What is the point of intersection for lines $y = 2x + 1$ and $y = -x + 4$?

Answer: $(1, 3)$. Solve the system by setting equations equal.

Flashcard 55: What is the equation of a line in slope-intercept form?

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

Flashcard 56: Identify the transformation applied: $y = (x - 1)^2 + 2$.

Answer: Right 1 unit, up 2 units. Vertex form shows horizontal and vertical shifts.

Flashcard 57: Identify the slope of the line: $3x - 4y = 12$.

Answer: $\frac{3}{4}$. Rearrange to $y = \frac{3}{4}x - 3$ to identify slope.

Flashcard 58: What is the slope of a line parallel to $y = -4x + 7$?

Answer: -4. Parallel lines have identical slopes.

Flashcard 59: Identify the center of the circle $(x - 3)^2 + (y + 4)^2 = 25$.

Answer: $(3, -4)$. Values of $(h, k)$ from standard form.

Flashcard 60: What are the coordinates of the x-intercept in the line $5x - 2y = 10$?

Answer: $(2, 0)$. Set $y = 0$ and solve for $x$.

Flashcard 61: Find the midpoint of the segment joining $(1, 2)$ and $(5, 6)$.

Answer: $(3, 4)$. Average the x-coordinates and y-coordinates: $\frac{1+5}{2}, \frac{2+6}{2}$.

Flashcard 62: What is the equation of a circle with center $(h, k)$ and radius $r$?

Answer: $(x - h)^2 + (y - k)^2 = r^2$. Standard circle equation with center $(h, k)$ and radius $r$.

Flashcard 63: What is the definition of a function in terms of ordered pairs?

Answer: Each input has exactly one output. Vertical line test ensures unique outputs.

Flashcard 64: Identify the y-intercept in the equation $y = 3x + 4$.

Answer:

1. The constant term when $x = 0$.

Flashcard 65: Identify the vertex of the parabola $y = (x - 3)^2 + 2$.

Answer: (3, 2). Vertex form $(x - h)^2 + k$ has vertex at $(h, k)$.

Flashcard 66: What is the equation of a horizontal line through point $(a, b)$?

Answer: $y = b$. All points have the same $y$-coordinate.

Flashcard 67: Identify the radius in the equation $(x - 2)^2 + (y + 1)^2 = 49$.

Answer: $7$. Square root of the constant gives radius.

Flashcard 68: What is the general form of the equation of a circle?

Answer: $x^2 + y^2 + Dx + Ey + F = 0$. Expanded form of circle equation.

Flashcard 69: State the formula for the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$.

Answer: $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. Pythagorean theorem applied to coordinate plane.

Flashcard 70: What is the vertex of the parabola $y = 3(x + 2)^2 - 5$?

Answer: $(-2, -5)$. Vertex form identifies $(h, k)$ directly.

Flashcard 71: Identify the intercepts of the quadratic $y = (x - 3)(x + 2)$.

Answer: x-intercepts: $3, -2$. Set $y = 0$ to find where parabola crosses $x$-axis.

Flashcard 72: State the formula for the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$.

Answer: $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. Pythagorean theorem applied to coordinate plane.

Flashcard 73: Identify the slope of the line given by $2y - 4x = 8$.

Answer:

1. Rearrange to $y = mx + b$ form first.

Flashcard 74: Which point lies on the line $y = 2x + 3$: (1, 5) or (2, 4)?

Answer: (1, 5). Substituting: $y = 2(1) + 3 = 5$, so point $(1, 5)$ satisfies the equation.

Flashcard 75: What does the slope of a line represent in a graph?

Answer: The rate of change or steepness of the line. Measures how much $y$ changes per unit increase in $x$.

Flashcard 76: What are the intercepts in the equation $y = \frac{1}{2}x - 3$?

Answer: x-intercept: 6, y-intercept: -3. Set each variable to zero alternately.

Flashcard 77: What is the general form of the equation of a parabola?

Answer: $y = ax^2 + bx + c$. Quadratic with degree 2 polynomial.

Flashcard 78: What is the equation for a line parallel to $y = 3x - 2$ passing through $(1, 4)$?

Answer: $y = 3x + 1$. Same slope, substitute point to find $b$.

Flashcard 79: What is the slope of a line parallel to $y = -4x + 7$?

Answer: -4. Parallel lines have identical slopes.

Flashcard 80: What does the slope of a line represent in a graph?

Answer: The rate of change or steepness of the line. Measures how much $y$ changes per unit increase in $x$.

Flashcard 81: What is the equation of a vertical line through point $(a, b)$?

Answer: $x = a$. All points have the same $x$-coordinate.

Flashcard 82: What is the equation of a circle with center $(h, k)$ and radius $r$?

Answer: $(x - h)^2 + (y - k)^2 = r^2$. Standard circle equation with center $(h, k)$ and radius $r$.

Flashcard 83: Identify the radius in the equation $(x - 2)^2 + (y + 1)^2 = 49$.

Answer:

1. Square root of the constant gives radius.

Flashcard 84: Which point lies on the line $y = 2x + 3$: (1, 5) or (2, 4)?

Answer: (1, 5). Substituting: $y = 2(1) + 3 = 5$, so point $(1, 5)$ satisfies the equation.

Flashcard 85: What is the point of intersection for lines $y = 2x + 1$ and $y = -x + 4$?

Answer: $(1, 3)$. Solve the system by setting equations equal.

Flashcard 86: What is the axis of symmetry for the parabola $y = ax^2 + bx + c$?

Answer: $x = -\frac{b}{2a}$. Vertical line through the vertex of the parabola.

Flashcard 87: What is the slope of a line perpendicular to $y = 2x + 3$?

Answer: $-\frac{1}{2}$. Negative reciprocal of the original slope.

Flashcard 88: Find the y-intercept of the line: $4x + 5y = 20$.

Answer:

1. Set $x = 0$: $5y = 20$, so $y = 4$.

Flashcard 89: Identify the slope of the line given by $2y - 4x = 8$.

Answer:

1. Rearrange to $y = mx + b$ form first.

Flashcard 90: What type of graph represents the equation $y = x^2$?

Answer: Parabola. Quadratic function creates U-shaped curve.

Flashcard 91: Which form of a line's equation uses the formula $y - y_1 = m(x - x_1)$?

Answer: Point-slope form. Uses a known point $(x_1, y_1)$ and slope $m$.

Flashcard 92: Identify the slope in the equation $y = -5x + 2$.

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

Flashcard 93: What are the coordinates of the x-intercept in the line $5x - 2y = 10$?

Answer: $(2, 0)$. Set $y = 0$ and solve for $x$.

Flashcard 94: What is the formula for the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$?

Answer: $\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. Pythagorean theorem applied to coordinate plane differences.

Flashcard 95: What is the general form of a quadratic function?

Answer: $ax^2 + bx + c = 0$. Standard form with highest power of 2.

Flashcard 96: What is the midpoint formula for the segment connecting $(x_1, y_1)$ and $(x_2, y_2)$?

Answer: $\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$. Average of the coordinates of the endpoints.

Flashcard 97: What is the formula for the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$?

Answer: $\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. Pythagorean theorem applied to coordinate plane differences.

Flashcard 98: What is the formula for converting a line from standard to slope-intercept form?

Answer: Solve $Ax + By = C$ for $y$. Isolate $y$ by dividing by coefficient of $y$.

Flashcard 99: Find the midpoint of the segment joining $(1, 2)$ and $(5, 6)$.

Answer: $(3, 4)$. Average the x-coordinates and y-coordinates: $\frac{1+5}{2}, \frac{2+6}{2}$.

Flashcard 100: What is the equation of a circle with center $(h, k)$ and radius $r$?

Answer: $(x - h)^2 + (y - k)^2 = r^2$. Distance from center to any point on circle.