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)