Slope intercept form. Formula , examples, video tutorial, and practice problems with explanation. (2024)

Worksheet(Worksheet with answer key on this page's topic)

Slope Intercept Form Calculator

Slope Intercept Applet

The slope intercept form is probably the most frequently used way to express equation of a line. To be able to use slope intercept form, all that you need to be able to do is 1) find the slope of a line and 2) find the y-intercept of a line.

Video Tutorial on Slope Intercept Form

The Formula

Slope intercept form. Formula , examples, video tutorial, and practice problems with explanation. (1)

In general, the slope intercept form assumes the formula: y = mx + b.

  • M is the slope(lesson on slope)
    • Mnemonic : 'm' means 'move'
  • B is the y-intercept(lesson on the y-intercept)
    • Mnemonic: 'b' means where the line begins.
Examples
  • y = 5x + 3 is an example of the Slope Intercept Form and represents the equation of a line with a slope of 5 and and a y-intercept of 3.
  • y = −2x + 6 represents the equation of a line with a slope of −2 and and a y-intercept of 6.

Vertical and Horizontal lines

Vertical Lines

The Equation of a vertical line is x = b.

Since a vertical line goes straight up and down, its slope is undefined. Also, the x value of every point on a vertical line is the same. Therefore, whatever the x value is, is also the value of 'b'.

For instance, the red line in the picture below is the graph of the x = 1.

Slope intercept form. Formula , examples, video tutorial, and practice problems with explanation. (2)

Horizontal Lines

The equation of a horizontal line is y = b where b is the y-intercept.

Since the slope of a horizontal line is 0, the general formula for the standard form equation, y = mx + b becomes y = 0x + b Slope intercept form. Formula , examples, video tutorial, and practice problems with explanation. (3) y = b. Also,since the line is horizontal, every point on that line has the exact same y value. This y-value is therefore also the y-intercept. For instance, the red line in the picture below is the graph of the horizontal line y = 1. (In depth lesson on the equation of a horizontal line)

Slope intercept form. Formula , examples, video tutorial, and practice problems with explanation. (4)

Practice Problems

Problem 1
Problem 2

Look at the picture of the graph below. Find the slope of this line, its y-intercept, then express the equation of this line in slope intercept form.

Slope intercept form. Formula , examples, video tutorial, and practice problems with explanation. (6)

What is the slope of the line ?

Step 1

What is the y-intercept of the line?

slope = $$ \frac{rise}{run} = \frac{-2}{1} = -2 $$

Step 2

What is the slope intercept form of this line?

-1 which is the y coordinate of the point (0, -1).

Step 3

What is the slope intercept form of the line pictured in the graph below?

The general formula is y = mx + b.

m = slope = -2
b = y-intercept of the line = -1

Therefore, the slope intercept form of this line is y = -2x - 1.

Problem 3

What is the slope intercept form of the line pictured in the graph below?

Slope intercept form. Formula , examples, video tutorial, and practice problems with explanation. (7)

m = slope of the line = $$ \frac{1}{2} $$

b = y-intercept of the line = 2.

Therefore, the equation of this line in slope intercept form is $$ y = \frac{1}{2} + 2 $$.

Problem 4

What is the slope intercept form of the line pictured in the graph below?

Slope intercept form. Formula , examples, video tutorial, and practice problems with explanation. (8)

The slope of a horizontal line = 0, because the there is no rise!

Therefore,

  • m = 0
  • b = y-intercept of the line = 1

Therefore, the equation of this line in slope intercept form is y = 0X + 1 $$ \Rightarrow $$ y = 1.

Practice Problems

Write the slope intercept form for the lines below.

Problem 6

A line with a slope of 3 and a y-intercept of -5.

In the general form:
y = mx + b
m = slope = 3
b = the y-intercept = -5

The slope intercept form of the equation:
y = 3x - 5

Problem 7

A line with a slope of ½ and a y-intercept of 7.

In the general form:
y = mx + b
m = slope = ½
b = the y intercept = 7

The slope intercept form of the equation:
y = ½x + 7

Worksheet(Worksheet with answer key on this page's topic)

Slope Intercept Form Calculator

Slope Intercept Applet

Linear Equations:

  • Slope of a Line
  • Y-intercept
  • Interactive Linear Equation
  • Equation Given Slope and a Point
  • Equation From Graph of a Line
  • Real World Applications
Slope intercept form. Formula , examples, video tutorial,  and practice problems with explanation. (2024)
Top Articles
Latest Posts
Recommended Articles
Article information

Author: Dan Stracke

Last Updated:

Views: 5845

Rating: 4.2 / 5 (63 voted)

Reviews: 86% of readers found this page helpful

Author information

Name: Dan Stracke

Birthday: 1992-08-25

Address: 2253 Brown Springs, East Alla, OH 38634-0309

Phone: +398735162064

Job: Investor Government Associate

Hobby: Shopping, LARPing, Scrapbooking, Surfing, Slacklining, Dance, Glassblowing

Introduction: My name is Dan Stracke, I am a homely, gleaming, glamorous, inquisitive, homely, gorgeous, light person who loves writing and wants to share my knowledge and understanding with you.