Slope-Intercept Form

**Slope-Intercept Form**

An equation is in **slope-intercept form**, if it is in the form:

*y* = *mx* + *b*

The line will always be a straight line with a slope of *m* and a *y*-intercept of (0, *b*).

**Example**

Determine the slope and *y*-intercept of the following line:

-4*x* + 2*y* = 16

**Solution**

Write the original equation in slope-intercept form by adding 4*x* to each side and then dividing everything by two:

-4*x* + 2*y* + 4*x* = 16 + 4*x*

(2*y*) / 2 = (4*x* + 16) / 2

*y* = 2*x* + 8

Therefore the slope is **2** and the *y*-intercept is **(0, 8)**, or **8**.

You can also use the slope and *y*-intercept to graph a line.

**Example**

Graph the equation: *y* = ^{1}/_{2}*x* + 3

**Solution**

Using the slope-intercept form we see that the *y*-intercept is 3, so the first point is at (0, 3)

The slope is ^{1}/_{2}, so we can plot a second point by moving up 1 unit and then to the right 2 units.

Finally we draw a line through both points.