Unit 4 · Topic 2

Slope-Intercept Form

Overview

Read slope and y-intercept straight from y = mx + b.

Topic 2 of 2~24 min
All units
Unit overview

The lesson

Read each section in order, work through every example on paper, then use the practice problems and quick check at the bottom.

y = mx + b

In slope-intercept form, m is the slope and b is the y-intercept (where the line crosses the y-axis).

Graphing from y = mx + b

  1. 1Plot the y-intercept (0, b) first.
  2. 2Use the slope as rise over run to plot a second point.
  3. 3Draw a line through the two points.
Worked example

Graph y = 2x + 3.

  1. 1y-intercept is 3, so plot (0, 3).
  2. 2Slope 2 = 2/1: go up 2 and right 1 to (1, 5).
  3. 3Draw the line through (0, 3) and (1, 5).

Why this matters

Read slope and y-intercept straight from y = mx + b.

These ideas show up on homework, quizzes, and the next unit in this grade. Getting comfortable here saves time later when the problems stack more steps together.

Common mistakes to avoid

Rushing to the answer without writing steps. Clear work helps you catch mistakes and shows your reasoning.

Re-reading the question too quickly. Underline what you are solving for before you start calculating.

Key ideas from this lesson

  1. y = mx + b
  2. Graphing from y = mx + b
  3. Plot the y-intercept (0, b) first.
  4. Use the slope as rise over run to plot a second point.
  5. Draw a line through the two points.

Video walkthroughs

Khan Academy

Slope-Intercept Form

Identify slope and y-intercept and graph the line.

Watch on YouTube
Khan Academy

Graphing a Line in Slope-Intercept Form

Graph a line using its slope and y-intercept.

Watch on YouTube
Khan Academy

Slope and y-Intercept from an Equation

Identify m and b in equations written in different forms.

Watch on YouTube
Khan Academy

Graphs of Linear Equations

Connect tables, equations, and graphs of linear functions.

Watch on YouTube

Practice

For each problem: write your work in the box, type your answer, and check it. If you are stuck, reveal the solution one step at a time. Do not skip straight to the final answer.

Exercise 1

Try it yourself

In y = 5x − 2, what are the slope and y-intercept?

Step-by-step solution

  1. 1m is the coefficient of x: slope = 5.
  2. 2b is the constant term: y-intercept = −2.
  3. 3Slope 5, y-intercept −2.

Exercise 2

Try it yourself

Write an equation with slope −2 and y-intercept 7.

Step-by-step solution

  1. 1m = −2 and b = 7.
  2. 2y = mx + b → y = −2x + 7.
  3. 3Equation: y = −2x + 7.

Exercise 3

Try it yourself

Graph y = (1/2)x + 4. What point is the y-intercept?

Step-by-step solution

  1. 1Set x = 0: y = 4.
  2. 2Plot (0, 4) on the y-axis.
  3. 3y-intercept: (0, 4).

Exercise 4

Try it yourself

A line has slope 3 and passes through (0, −1). Write its equation.

Step-by-step solution

  1. 1Slope m = 3, y-intercept b = −1.
  2. 2y = 3x − 1.
  3. 3Equation: y = 3x − 1.

Exercise 5

Try it yourself

Rewrite 2x + y = 10 in slope-intercept form.

Step-by-step solution

  1. 1Subtract 2x from both sides: y = −2x + 10.
  2. 2Slope is −2, y-intercept is 10.
  3. 3y = −2x + 10.

Re-read the lesson section if you get stuck, then try again without peeking at the solution.

Khan Academy

Slope-intercept form

Open resource

Quick check

Answer all questions. Retake the quiz until you feel confident before moving on.

Slope-Intercept Form

Question 1 of 4

Easy

In y = -3x + 5, what is the slope?

1-on-1 tutoring

Stuck on something specific?

Adam & Alan can walk through it live. Free consultation call for new clients.

Book a tutoring session