Linear Functions

What you'll learn

Determine slope and intercepts from an equation or graph
Write and graph linear functions in slope-intercept form
Model real-world situations with linear functions

Words to know

Function —: a rule giving exactly one output for each input
Slope —: the rate of change, rise over run
y-intercept —: where the line crosses the y-axis
Slope-intercept form —: y = mx + b
Rate of change —: how fast the output changes per unit of input
Linear —: graphs as a straight line

Why it matters Linear functions describe anything that changes at a steady rate, like distance over time or savings that grow by a fixed amount each week.

Worked examples

Model ItI do

Graph y = 2x + 1 and state the slope and y-intercept.

The y-intercept is 1, so start at (0, 1). The slope is 2, so go up 2 and right 1 to (1, 3) and draw the line.

Try It TogetherWe do

Find the slope of the line through (1, 3) and (3, 7).

Slope = (7 - 3) / (3 - 1) = 4 / 2 = 2. The line rises 2 for every 1 it runs right.

Now YouYou do

Write the equation of a line with slope 3 and y-intercept -2.

Substitute the slope and intercept into y = mx + b. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

1.State the slope of y = 6x + 2.
2.State the y-intercept of y = 3x - 5.
3.Write the equation with slope 4 and y-intercept 0.

On Level

The core Quick Check from the book.

1.State the slope of y = -4x + 7.
2.State the y-intercept of y = (1/2)x - 3.
3.Find the slope through (0, 1) and (2, 5).
4.Write the equation with slope 5 and y-intercept 0.
5.Is y = 3x + 2 increasing or decreasing?

Challenge

Stretch your thinking.

1.Find the slope of the line through (2, 1) and (6, 9).
2.Write the equation of the line through (0, 4) with slope -3.
3.A line passes through (1, 5) and (4, 5). What is its slope?