SAT Math Flashcards: Linear Functions

What this deck covers

This deck focuses on Linear Functions, 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: State the standard form of a linear equation.

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

Flashcard 2: 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 3: Write the equation of the line with slope 3 and y-intercept -4.

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

Flashcard 4: If $y = -x + 2$ is shifted right by 2 units, what is the new equation?

Answer: $y = -(x - 2) + 2$. Horizontal shift affects the $x$-term inside parentheses.

Flashcard 5: If $y = 2x + 5$ is shifted up by 3 units, what is the new equation?

Answer: $y = 2x + 8$. Vertical shift changes only the y-intercept.

Flashcard 6: What is the equation of a vertical line through $(5, -2)$?

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

Flashcard 7: What is the x-intercept of the line $2x + 5y = 10$?

Answer:

1. Set $y = 0$ to get $2x = 10$, so $x = 5$.

Flashcard 8: What is the x-intercept of the line $2x + 5y = 10$?

Answer:

1. Set $y = 0$ to get $2x = 10$, so $x = 5$.

Flashcard 9: Find the slope of the line through points $(1, 2)$ and $(3, 6)$.

Answer:

1. $m = \frac{6-2}{3-1} = \frac{4}{2} = 2$

Flashcard 10: What is the x-intercept of the line $y = 2x - 4$?

Answer:

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

Flashcard 11: Determine if the lines $y = 2x + 3$ and $y = 2x - 4$ are parallel.

Answer: Yes, they are parallel. Both lines have slope 2, so they're parallel.

Flashcard 12: State the standard form of a linear equation.

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

Flashcard 13: What is the slope of any horizontal line?

Answer:

1. No vertical change means zero slope.

Flashcard 14: Determine if the lines $y = 3x + 1$ and $y = -\frac{1}{3}x + 2$ are perpendicular.

Answer: Yes, they are perpendicular. Slopes are 3 and $-\frac{1}{3}$; their product is -1.

Flashcard 15: What is the equation of a horizontal line through $(3, 7)$?

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

Flashcard 16: Identify the slope of the line parallel to $y = \frac{1}{2}x - 4$.

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

Flashcard 17: What condition must be true for lines to be parallel?

Answer: The slopes are equal. Lines with identical slopes never intersect.

Flashcard 18: Find the x-intercept of the line $2x + 3y = 6$.

Answer:

1. Set $y = 0$ and solve for $x$.

Flashcard 19: What does the 'b' represent in the equation $y = mx + b$?

Answer: Y-intercept of the line. The constant term where the line crosses the y-axis.

Flashcard 20: Find the midpoint of the segment connecting $(2, 3)$ and $(4, 5)$.

Answer: $(3, 4)$. Use midpoint formula with given coordinates.

Flashcard 21: What is the point-slope form of a linear equation?

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

Flashcard 22: If $y = 2x + 5$ is shifted up by 3 units, what is the new equation?

Answer: $y = 2x + 8$. Vertical shift changes only the y-intercept.

Flashcard 23: Identify the slope in the equation $y = 3x + 7$.

Answer:

1. The coefficient of $x$ is the slope.

Flashcard 24: What is the midpoint formula for points $(x_1, y_1)$ and $(x_2, y_2)$?

Answer: $\bigg( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \bigg)$. Average of coordinates for both $x$ and $y$ values.

Flashcard 25: Given point $(1, 2)$ and slope 4, find the equation in point-slope form.

Answer: $y - 2 = 4(x - 1)$. Substitute point coordinates and slope into formula.

Flashcard 26: Find the slope of the line through points $(1, 2)$ and $(3, 6)$.

Answer:

1. $m = \frac{6-2}{3-1} = \frac{4}{2} = 2$

Flashcard 27: Convert $y = -2x + 5$ to standard form.

Answer: $2x + y = 5$. Add $2x$ to both sides to get standard form.

Flashcard 28: What is the point-slope form of a linear equation?

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

Flashcard 29: Identify the slope in the equation $y = -3x + 7$.

Answer: -3. The coefficient of $x$ is the slope.

Flashcard 30: Convert the equation $3x - 2y = 6$ to slope-intercept form.

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

Flashcard 31: Convert $y = 4x - 3$ to standard form.

Answer: $4x - y = 3$. Move $y$ to left side and arrange coefficients properly.

Flashcard 32: Convert $y = -2x + 5$ to standard form.

Answer: $2x + y = 5$. Add $2x$ to both sides to get standard form.

Flashcard 33: Identify the slope in the equation $y = -3x + 7$.

Answer: -3. The coefficient of $x$ is the slope.

Flashcard 34: What is the equation of a horizontal line through $(3, 7)$?

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

Flashcard 35: 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 36: Identify the y-intercept in the equation $3y = 12x + 6$.

Answer:

1. Divide by 3: $y = 4x + 2$, so y-intercept is 2.

Flashcard 37: 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 38: Write the equation of the line with slope 3 and y-intercept -4.

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

Flashcard 39: Determine if the lines $y = 3x + 1$ and $y = -\frac{1}{3}x + 2$ are perpendicular.

Answer: Yes, they are perpendicular. Slopes are 3 and $-\frac{1}{3}$; their product is -1.

Flashcard 40: Determine the y-intercept of the line $y = -4x + 5$.

Answer:

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

Flashcard 41: What is the x-intercept of the line $y = 2x - 4$?

Answer:

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

Flashcard 42: 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 43: Find the x-intercept of the line $2x + 3y = 6$.

Answer:

1. Set $y = 0$ and solve for $x$.

Flashcard 44: Find the y-intercept of the line $5x + 3y = 15$.

Answer:

1. Set $x = 0$ to get $3y = 15$, so $y = 5$.

Flashcard 45: If $y = -x + 2$ is shifted right by 2 units, what is the new equation?

Answer: $y = -(x - 2) + 2$. Horizontal shift affects the $x$-term inside parentheses.

Flashcard 46: What is the slope of any vertical line?

Answer: Undefined. Division by zero makes slope undefined.

Flashcard 47: What is the standard form of a linear equation?

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

Flashcard 48: State the point-slope form of a linear equation.

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

Flashcard 49: Identify the y-intercept in the equation $y = 2x - 7$.

Answer: -7. The constant term in slope-intercept form.

Flashcard 50: What is the midpoint formula for points $(x_1, y_1)$ and $(x_2, y_2)$?

Answer: $\bigg( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \bigg)$. Average of coordinates for both $x$ and $y$ values.

Flashcard 51: Identify the slope in the equation $y = -3x + 5$.

Answer: -3. The coefficient of $x$ in slope-intercept form.

Flashcard 52: What is the equation of a vertical line through $(5, -2)$?

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

Flashcard 53: Determine the y-intercept of the line $y = -4x + 5$.

Answer:

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

Flashcard 54: What condition must be true for lines to be perpendicular?

Answer: Product of slopes is -1. Negative reciprocals create 90-degree intersections.

Flashcard 55: Given point $(1, 2)$ and slope 4, find the equation in point-slope form.

Answer: $y - 2 = 4(x - 1)$. Substitute point coordinates and slope into formula.

Flashcard 56: State the formula for calculating slope given two points.

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

Flashcard 57: State the formula for finding the slope 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: Find the y-intercept of the line $5x + 3y = 15$.

Answer:

1. Set $x = 0$ to get $3y = 15$, so $y = 5$.

Flashcard 59: What is the standard form of a linear equation?

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

Flashcard 60: What condition must be true for lines to be perpendicular?

Answer: Product of slopes is -1. Negative reciprocals create 90-degree intersections.

Flashcard 61: What does the 'm' represent in the equation $y = mx + b$?

Answer: Slope of the line. The coefficient of $x$ that determines steepness and direction.

Flashcard 62: Identify the slope of the line parallel to $y = \frac{1}{2}x - 4$.

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

Flashcard 63: Find the midpoint of the segment connecting $(2, 3)$ and $(4, 5)$.

Answer: $(3, 4)$. Use midpoint formula with given coordinates.

Flashcard 64: What does the 'm' represent in the equation $y = mx + b$?

Answer: Slope of the line. The coefficient of $x$ that determines steepness and direction.

Flashcard 65: Find the slope of a line through points $(2, 3)$ and $(4, 7)$.

Answer:

1. Use $m = \frac{7-3}{4-2} = \frac{4}{2} = 2$.

Flashcard 66: Determine if the lines $y = 2x + 3$ and $y = 2x - 4$ are parallel.

Answer: Yes, they are parallel. Both lines have slope 2, so they're parallel.

Flashcard 67: What is the standard form of a linear equation?

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

Flashcard 68: Find the x-intercept of the line $4x - 8y = 16$.

Answer:

1. Set $y = 0$ to get $4x = 16$, so $x = 4$.

Flashcard 69: Find the equation of a line with slope 2 passing through (1, -3).

Answer: $y + 3 = 2(x - 1)$. Substitute the point and slope into point-slope form.

Flashcard 70: Identify the y-intercept in the equation $y = 2x - 7$.

Answer: -7. The constant term in slope-intercept form.

Flashcard 71: Calculate the slope of the line $y = -\frac{2}{3}x + 4$.

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

Flashcard 72: Which term represents the y-intercept in $y = 5x + 9$?

Answer:

1. The constant term is the y-intercept.

Flashcard 73: What is the point-slope form of a linear equation?

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

Flashcard 74: Convert $y = 4x - 3$ to standard form.

Answer: $4x - y = 3$. Move $y$ to left side and arrange coefficients properly.

Flashcard 75: Calculate the slope of the line $y = -\frac{2}{3}x + 4$.

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

Flashcard 76: State the formula for calculating the slope between two points.

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

Flashcard 77: Which term represents the y-intercept in $y = 5x + 9$?

Answer:

1. The constant term is the y-intercept.

Flashcard 78: State the formula for calculating slope given two points.

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

Flashcard 79: State the formula for calculating the slope between two points.

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

Flashcard 80: State the formula for finding the slope 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 81: Convert $3x + 4y = 12$ to slope-intercept form.

Answer: $y = -\frac{3}{4}x + 3$. Isolate $y$ by dividing both sides by 4.

Flashcard 82: Convert the equation $3x - 2y = 6$ to slope-intercept form.

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

Flashcard 83: Identify the slope in the equation $y = -3x + 5$.

Answer: -3. The coefficient of $x$ in slope-intercept form.

Flashcard 84: What is the slope of any vertical line?

Answer: Undefined. Division by zero makes slope undefined.

Flashcard 85: What is the standard form of a linear equation?

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

Flashcard 86: What does the 'b' represent in the equation $y = mx + b$?

Answer: Y-intercept of the line. The constant term where the line crosses the y-axis.

Flashcard 87: What is the slope of any horizontal line?

Answer:

1. No vertical change means zero slope.

Flashcard 88: 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 89: Determine the slope of the line $3x - 2y = 6$.

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

Flashcard 90: Identify the slope in the equation $y = 3x + 7$.

Answer:

1. The coefficient of $x$ is the slope.

Flashcard 91: Find the x-intercept of the line $4x - 8y = 16$.

Answer:

1. Set $y = 0$ to get $4x = 16$, so $x = 4$.

Flashcard 92: Identify the y-intercept in the equation $3y = 12x + 6$.

Answer:

1. Divide by 3: $y = 4x + 2$, so y-intercept is 2.

Flashcard 93: What condition must be true for lines to be parallel?

Answer: The slopes are equal. Lines with identical slopes never intersect.

Flashcard 94: Find the equation of a line with slope 2 passing through (1, -3).

Answer: $y + 3 = 2(x - 1)$. Substitute the point and slope into point-slope form.

Flashcard 95: 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 96: State the point-slope form of a linear equation.

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

Flashcard 97: What is the point-slope form of a linear equation?

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