## Slope-Intercept Form

There are several forms that the equation of a line can take. They may look different, but they all describe the same line--a line can be described by many equations. All (linear) equations describing a particular line, however, are equivalent.

The first of the forms for a linear equation is slope-intercept form. Equations in slope-intercept form look like this:

where

*m* is the slope of the line and

*b* is the y-intercept of the line, or the y-coordinate of the point at which the line crosses the y-axis.

To write an equation in slope-intercept form, given a graph of that equation, pick two points on the line and use them to find the slope. This is the value of *m* in the equation. Next, find the coordinates of the *y*-intercept--this should be of the form (0, *b*). The *y*- coordinate is the value of *b* in the equation.

Finally, write the equation, substituting numerical values in for *m* and *b*. Check your equation by picking a point on the line (not the *y*-intercept) and plugging it in to see if it satisfies the equation.

*Example 1*: Write an equation of the following line in slope-intercept form:

Graph of a Line

First, pick two points on the line--for example,

(2, 1) and

(4, 0). Use these points to calculate the slope:

*m* = = = - .

Next, find the

*y*-intercept:

(0, 2). Thus,

*b* = 2.

Therefore, the equation for this line is

*y* = - *x* + 2.

Check using the point

(4, 0):

0 = - (4) + 2 ? Yes.

*Example 2*: Write an equation of the line with slope *m* = which crosses the *y*-axis at (0, - ).

*y* = *x* -