﻿ Slope intercept form. Formula , examples, video tutorial, and practice problems with explanation. # 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

##### 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.

#### 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)

### Practice Problems

##### Problem 2
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

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

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 $$\Rightarrow$$ y = 1.

### Practice Problems

Write the slope intercept form for the lines below.

##### Problem 6

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

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