Slope & Intercepts
What is the slope of y = 3x + 5?
3
What is the slope of y = -1/2x + 6?
- 1/2
What type of transformation is g(x) = x + 4?
Vertical translation up by 4 units.
Convert x + y = 5 to slope-intercept form.
y = -x + 5
A taxi charges a $3 starting fee plus $2 every mile traveled. Write an equation in slope-intercept form to represent the cost, y, after x miles.
y = 2x + 3
What is the y-intercept of y = -2x + 7
7
Graph y = 4x - 1. What is the y-intercept?
-1
What transformation is g(x) = -x?
Reflection across the x-axis.
Convert 9x - 3y = 12 into slope-intercept form.
y = 3x - 4
y = 3x + 8
Write the slope-intercept form of a line where the slope = 4 and the y-intercept = -1
y = 4x - 1
Given a line with slope -2 and y-intercept 3, write the equation in slope-intercept form.
y = -2x + 3
Compare g(x) = 1/2x to y = x
g(X) represents a vertical compression.
Convert -10x + 5y = 25 into slope-intercept form.
y = 2x + 5
A phone plan charges $25 a month plus $0.05 for every text message sent. Write an equation in slope-intercept form for the monthly cost, y, if x texts are sent.
y = 0.05x + 25
Convert -10x + 5y = 25 into slope-intercept form.
y = 2x + 5
Graph 9x - 3y = 12. What is the slope?
3
What transformation happens in g(x) = x - 7?
Horizontal shift to the right by 7 units.
y = -1/4x - 3
At Chipotle, a burrito bowl costs $9. Every extra topping (like guac, queso, or double meat) adds $2 each. Write an equation for the total cost, y, if you buy a burrito bowl with x extra toppings. Then find the cost if you add 4 toppings.
Equation: y = 2x + 9
Cost: $17
Convert 2x + 8y = -24 into slope-intercept form.
y = -1/4x - 3
How does doubling the slope of a line change its graph?
It become steeper. (Compression)
Which transformation is a vertical stretch? Give an example.
Multiplying the slope by a number greater than 1. (e.g. y = 5x)
What is the formula for slope-intercept form?
y = mx + b
A concert ticket costs $80 plus a $10 service fee. If you also buy merch, each item costs $25. Write an equation in slope-intercept form for the total cost, y, if you buy x merch items along with your ticket. Then, find the total if you buy 3 merch items.
Equation: y = 25x + 90
Cost: $165