Algebra I
Lesson 2 of 4 8 min +60 XP

Slope & Linear Functions

Read and graph y = mx + b.

What you'll learn

  • Interpret slope as rise over run
  • Identify the y-intercept
  • Read slope from an equation
The wheelchair ramp

A ramp that rises 1 foot for every 4 feet it runs has a slope of 1/4 — steeper ramps climb faster. In y = mx + b, m is that steepness and b is where the ramp starts off the ground; the whole line is just the ramp's path.

Slope-intercept form

A line can be written y = mx + b, where m is the slope (steepness) and b is the y-intercept (where the line crosses the y-axis).

Slope = rise / run

A slope of 2 means y increases by 2 each time x increases by 1.

Simulation · Line grapher: y = mx + b

y = 1x + 2

Drag the slope and intercept to see how each one moves the line.

Lab · Find the rule
  1. Set the slope (m) to 2 and the intercept (b) to 1.
  2. Read the point where the line crosses the y-axis — that's b.
  3. Move 1 step right and count how many steps up the line goes — that's m.
  4. Now set m to a negative value and watch the line tilt the other way.

What you should see: The purple dot sits at (0, b) and the line rises by m for every step right. A negative slope falls instead of rises.

Knowledge Check

+15 XP / correct

1. In y = 3x − 4, what is the slope?

2. In y = 3x − 4, where does the line cross the y-axis?