Linear Functions - ACT Math
Card 1 of 30
Identify the slope of the line $3y - 9x = 12$.
Identify the slope of the line $3y - 9x = 12$.
Tap to reveal answer
- Rewrite as $y = 3x + 4$; slope is $3$.
- Rewrite as $y = 3x + 4$; slope is $3$.
← Didn't Know|Knew It →
What is the equation of the line with slope $2$ passing through $(3,-1)$ in point-slope form?
What is the equation of the line with slope $2$ passing through $(3,-1)$ in point-slope form?
Tap to reveal answer
$y+1=2(x-3)$. Direct substitution into point-slope form.
$y+1=2(x-3)$. Direct substitution into point-slope form.
← Didn't Know|Knew It →
What is the equation of the line through points $(2,1)$ and $(2,5)$?
What is the equation of the line through points $(2,1)$ and $(2,5)$?
Tap to reveal answer
$x=2$. Same $x$-coordinate means vertical line.
$x=2$. Same $x$-coordinate means vertical line.
← Didn't Know|Knew It →
What is the slope of the line $y=-7$?
What is the slope of the line $y=-7$?
Tap to reveal answer
$0$. Horizontal line has zero slope.
$0$. Horizontal line has zero slope.
← Didn't Know|Knew It →
What is the average rate of change of $f(x)=-3x+2$ from $x=1$ to $x=4$?
What is the average rate of change of $f(x)=-3x+2$ from $x=1$ to $x=4$?
Tap to reveal answer
$-3$. For linear functions, rate of change equals slope.
$-3$. For linear functions, rate of change equals slope.
← Didn't Know|Knew It →
What is the equation in slope-intercept form of the line with slope $3$ and $y$-intercept $-2$?
What is the equation in slope-intercept form of the line with slope $3$ and $y$-intercept $-2$?
Tap to reveal answer
$y=3x-2$. Direct substitution into $y=mx+b$.
$y=3x-2$. Direct substitution into $y=mx+b$.
← Didn't Know|Knew It →
What is the equation of the line through $(2, -1)$ with slope $\frac{1}{2}$?
What is the equation of the line through $(2, -1)$ with slope $\frac{1}{2}$?
Tap to reveal answer
$y + 1 = \frac{1}{2}(x - 2)$. Point-slope form with given point and slope.
$y + 1 = \frac{1}{2}(x - 2)$. Point-slope form with given point and slope.
← Didn't Know|Knew It →
What is $x$ if the point $(x,9)$ lies on the line $y=2x+1$?
What is $x$ if the point $(x,9)$ lies on the line $y=2x+1$?
Tap to reveal answer
$4$. Solve: $9=2x+1$, so $x=4$.
$4$. Solve: $9=2x+1$, so $x=4$.
← Didn't Know|Knew It →
What is $f(5)$ if $f(x)=2x-3$?
What is $f(5)$ if $f(x)=2x-3$?
Tap to reveal answer
$7$. Substitute: $f(5)=2(5)-3=7$.
$7$. Substitute: $f(5)=2(5)-3=7$.
← Didn't Know|Knew It →
What is the slope of the line given by the equation $4x - 2y = 8$?
What is the slope of the line given by the equation $4x - 2y = 8$?
Tap to reveal answer
- Rewrite as $y = 2x - 4$; slope is $2$.
- Rewrite as $y = 2x - 4$; slope is $2$.
← Didn't Know|Knew It →
What is the equation of a line passing through $(0, -2)$ with slope $-3$?
What is the equation of a line passing through $(0, -2)$ with slope $-3$?
Tap to reveal answer
$y = -3x - 2$. Line passes through $(0, -2)$ with given slope.
$y = -3x - 2$. Line passes through $(0, -2)$ with given slope.
← Didn't Know|Knew It →
Identify the slope of the line $3y - 9x = 12$.
Identify the slope of the line $3y - 9x = 12$.
Tap to reveal answer
- Rewrite as $y = 3x + 4$; slope is $3$.
- Rewrite as $y = 3x + 4$; slope is $3$.
← Didn't Know|Knew It →
What is the equation of a line with slope 2 passing through $(1, 3)$?
What is the equation of a line with slope 2 passing through $(1, 3)$?
Tap to reveal answer
$y - 3 = 2(x - 1)$. Point-slope form: $y - y_1 = m(x - x_1)$.
$y - 3 = 2(x - 1)$. Point-slope form: $y - y_1 = m(x - x_1)$.
← Didn't Know|Knew It →
Find the slope of a vertical line.
Find the slope of a vertical line.
Tap to reveal answer
Undefined. Division by zero in slope formula.
Undefined. Division by zero in slope formula.
← Didn't Know|Knew It →
Find the slope of a horizontal line.
Find the slope of a horizontal line.
Tap to reveal answer
- No vertical change means slope equals zero.
- No vertical change means slope equals zero.
← Didn't Know|Knew It →
What is the slope of a line perpendicular to the line $y = -3x + 4$?
What is the slope of a line perpendicular to the line $y = -3x + 4$?
Tap to reveal answer
$\frac{1}{3}$. Negative reciprocal of $-3$ is $\frac{1}{3}$.
$\frac{1}{3}$. Negative reciprocal of $-3$ is $\frac{1}{3}$.
← Didn't Know|Knew It →
What is the slope of a line parallel to the line $y = \frac{5}{2}x + 1$?
What is the slope of a line parallel to the line $y = \frac{5}{2}x + 1$?
Tap to reveal answer
$\frac{5}{2}$. Parallel lines have identical slopes.
$\frac{5}{2}$. Parallel lines have identical slopes.
← Didn't Know|Knew It →
Convert the equation $y = -2x + 5$ to standard form.
Convert the equation $y = -2x + 5$ to standard form.
Tap to reveal answer
$2x + y = 5$. Move $x$ term: $2x + y = 5$.
$2x + y = 5$. Move $x$ term: $2x + y = 5$.
← Didn't Know|Knew It →
What is the y-intercept of the equation $4x + 2y = 8$?
What is the y-intercept of the equation $4x + 2y = 8$?
Tap to reveal answer
- Set $x = 0$: $2y = 8$, so $y = 4$.
- Set $x = 0$: $2y = 8$, so $y = 4$.
← Didn't Know|Knew It →
What is the x-intercept of the equation $y = 3x + 9$?
What is the x-intercept of the equation $y = 3x + 9$?
Tap to reveal answer
-3. Set $y = 0$: $0 = 3x + 9$, so $x = -3$.
-3. Set $y = 0$: $0 = 3x + 9$, so $x = -3$.
← Didn't Know|Knew It →
Determine if the lines $y = -\frac{1}{2}x + 1$ and $y = 2x - 3$ are perpendicular.
Determine if the lines $y = -\frac{1}{2}x + 1$ and $y = 2x - 3$ are perpendicular.
Tap to reveal answer
Yes. Slopes are $-\frac{1}{2}$ and $2$; their product is $-1$.
Yes. Slopes are $-\frac{1}{2}$ and $2$; their product is $-1$.
← Didn't Know|Knew It →
Determine if the lines $y = 2x + 3$ and $y = 2x - 4$ are parallel.
Determine if the lines $y = 2x + 3$ and $y = 2x - 4$ are parallel.
Tap to reveal answer
Yes. Both have slope $2$, so they're parallel.
Yes. Both have slope $2$, so they're parallel.
← Didn't Know|Knew It →
Convert the equation $2x + 3y = 6$ to slope-intercept form.
Convert the equation $2x + 3y = 6$ to slope-intercept form.
Tap to reveal answer
$y = -\frac{2}{3}x + 2$. Solve for $y$: $3y = -2x + 6$, so $y = -\frac{2}{3}x + 2$.
$y = -\frac{2}{3}x + 2$. Solve for $y$: $3y = -2x + 6$, so $y = -\frac{2}{3}x + 2$.
← Didn't Know|Knew It →
Find the slope between points $(2, 3)$ and $(4, 7)$.
Find the slope between points $(2, 3)$ and $(4, 7)$.
Tap to reveal answer
- Using slope formula: $\frac{7-3}{4-2} = \frac{4}{2} = 2$.
- Using slope formula: $\frac{7-3}{4-2} = \frac{4}{2} = 2$.
← Didn't Know|Knew It →
State the formula to calculate the slope between two points $(x_1, y_1)$ and $(x_2, y_2)$.
State the formula to calculate the slope between two points $(x_1, y_1)$ and $(x_2, y_2)$.
Tap to reveal answer
$m = \frac{y_2 - y_1}{x_2 - x_1}$. Rise over run between any two points.
$m = \frac{y_2 - y_1}{x_2 - x_1}$. Rise over run between any two points.
← Didn't Know|Knew It →
Identify the y-intercept in the equation $y = 4x - 7$.
Identify the y-intercept in the equation $y = 4x - 7$.
Tap to reveal answer
-7. Constant term in slope-intercept form.
-7. Constant term in slope-intercept form.
← Didn't Know|Knew It →
Identify the slope in the equation $y = -3x + 5$.
Identify the slope in the equation $y = -3x + 5$.
Tap to reveal answer
-3. Coefficient of $x$ in slope-intercept form.
-3. Coefficient of $x$ in slope-intercept form.
← Didn't Know|Knew It →
What does the variable $b$ represent in the equation $y = mx + b$?
What does the variable $b$ represent in the equation $y = mx + b$?
Tap to reveal answer
The y-intercept of the line. Constant term where line crosses y-axis at $(0, b)$.
The y-intercept of the line. Constant term where line crosses y-axis at $(0, b)$.
← Didn't Know|Knew It →
What does the variable $m$ represent in the equation $y = mx + b$?
What does the variable $m$ represent in the equation $y = mx + b$?
Tap to reveal answer
The slope of the line. Coefficient of $x$ determines steepness and direction.
The slope of the line. Coefficient of $x$ determines steepness and direction.
← Didn't Know|Knew It →
What is the slope-intercept form of a linear equation?
What is the slope-intercept form of a linear equation?
Tap to reveal answer
$y = mx + b$. Form showing slope $m$ and y-intercept $b$ directly.
$y = mx + b$. Form showing slope $m$ and y-intercept $b$ directly.
← Didn't Know|Knew It →