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

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.

### 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.

#### 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

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

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

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

y = mx + b

y = 1x + 2

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

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

What is the slope intercept form of this line?

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

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

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 $$ y = \frac{1}{2} +2 $$

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.

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

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

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