Unit 3 · Slope, Rate of Change & Linear Equations
A linear function can be a table, a graph, a verbal description, or an equation. All four must tell the same story.
y = mx + b. m is the slope; b is the y-intercept, the value of y when x = 0. In a context, b is often a starting amount and m is the ongoing rate.
Find m, then substitute one point into y = mx + b to solve for b. Check with the second point.
The point where a graph crosses the y-axis; the value of y when x = 0.
Example: In y = −3x + 7, the y-intercept is 7.
Try the prompt first. The steps stay folded until you ask to see them.
A MetroCard starts with $33.00. Each ride costs $2.90. Write a function for remaining value v after r rides.
Watch for
Mixing up which quantity is slope
Slope is the rate, not the starting amount.
Fix: Ask: what happens each time the input increases by 1?
Submit each answer to check it. The key is not shown until you do.
Which equation represents the graph of a line on a coordinate plane that passes through the x-intercept at (9, 0) and the y-intercept at (0, −5)?
Cory drinks water from a bottle during a bike ride. The average amount of water, in ounces, in his water bottle can be represented by the equation y = −8x + 32, where y is the amount of water remaining after x hours. Based on the equation, what amount of water, in ounces, will remain in the bottle after Cory rides for 2 1/2 hours?
The equation that represents the sequence −2, −5, −8, −11, −14, … is
Build a table first: input 0, 1, 2, then read b and m from the table.
Convert the same line among slope-intercept, point-slope, and standard form.
Sentence starters · Notice and Wonder · Three Reads · Think-Pair-Share · Compare and Connect · Math Talk · Stronger and Clearer Each Time