Slope and Rate of Change
What is the slope of a line that passes through the points (1, 2) and (3, 8)?
3
Write the equation of a line in slope-intercept form with a slope of 2 passing through (0, -4).
y = 2x - 4
Plot and identify the y-intercept of y = -2x + 4.
y-intercept is 4.
A rental company charges $5 per hour plus a $20 flat fee. Write an equation for the cost C as a function of time t.
C = 5t + 20
Find the y-intercept of the equation 3x - 6y = 12.
-2
Determine the rate of change from the graph of a line passing through points (4, -2) and (8, 6).
2
Convert the point-slope form equation y - 3 = 4(x + 2) to slope-intercept form.
y = 4x + 11
Graph y + 3 = -1(x - 5) and state the slope and y-intercept.
Slope = -1, y-intercept = -2.
A scooter rental charges $3.25 for the first minute and $0.25 for each additional minute. Write a linear equation to represent the cost.
C = 3.25 + 0.25(t - 1)
What is the x-intercept of the graph of y = 2x + 10?
-5
Write the slope-intercept form of a line with a slope of 5 and a y-intercept of -3.
y=5x-3
Write the equation of a line in standard form that passes through (5, -1) with a slope of -3.
3x + y = 14
Given the table of values x: 0, 1, 2; y: 3, 5, 7, determine the equation of the line.
y = 2x + 3
Jordan earns $24.75 plus $0.20 for every house she delivers to. Write an equation and identify the slope and y-intercept.
y = 0.2x + 24.75, slope = 0.2, y-intercept = 24.75.
Write a direct variation equation if y = 14 when x = 7.
y=2x
If a sequence increases by 2 every step starting at 1, what is the slope of its corresponding linear function?
2
Create the equation of a line perpendicular to y = -1/2x + 7 that passes through (2, 5).
y = 2x + 1
Identify the x-intercept and y-intercept of the graph of 2x + 3y = 6.
x-intercept = 3, y-intercept = 2.
A florist sells carnations for $11 per dozen and lilies for $13 per dozen. Write an equation for total earnings if they sell x dozens of carnations and y dozens of lilies.
11x + 13y = Total Earnings
Solve for the x-intercept and y-intercept of -5x + 4y = 20.
x-intercept = 4, y-intercept = -5.
Given the equation y = 3/4x - 5, calculate the slope and interpret its meaning in a real-world context.
Slope is 3/4, meaning for every 4 units horizontally, the line rises 3 units vertically.
Find the equation of a line parallel to y = 4x - 9 passing through the point (6, -2).
y = 4x - 26
Sketch the graph of y = -2/3x + 4 and explain the transformation from y = x.
A vertical shrink by factor 2/3 and shift up 4.
A booster club sells tickets for $4 (students) and $8 (adults) to raise $200. Write an equation representing ticket sales.
4x + 8y = 200
Given y varies directly with x and y = 30 when x = 10, find y when x = 50.
y = 150