Slope Intercept Form

A way to express the equation of a line

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

General Formula for Slope Intercept Equation

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

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.

Slope Intercept Equation of

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.

Picture of Vertical Line Graph

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 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)

Picture of Horizontal Line

Practice Problems

Problem 1

What is the slope intercept form of the lines graphed below?

Slope intercept form of linear equation
Step 1

What is the slope of the line below?

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

Step 2

What is the y-intercept of the line on the left?

2 or the y value of the point (0,2)

Step 3

What is the slope-intercept form of this line's equation?

y = mx + b
y = 1x + 2

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 of graph of line

What is the slope of the line on the left?

Step 1

What is the y-intercept of the line on the left?

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 of Line in graph

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 of Line in graph

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

Therefore,


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

Practice Problems

Write the slope intercept form for the lines below.

Problem 5

A line with a slope of 2 and a y-intercept of 12

In the general form
y = mx + b
m = slope = 2
b = the y intercept = 12

The slope intercept form of the equation:
y = 2x + 12

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