# Slope-Intercept Form

Multiplying both sides of the equation  by x â€“ a yields

y â€“ b = m(x â€“ a)

Now, if the line passes through the y-axis at (0,b), then the equation becomes

y â€“ b = m(x â€“ 0)

or

y â€“ b = mx

or

y = mx + b

This is called the slope-intercept form of the equation of a line, where m is the slope and b is the y-intercept. This form is convenient because it displays the two most important bits of information about a line: its slope and its y-intercept.

Example

The equation of the line above is . Which one of the following must be true about line segments AO and BO ?

1. AO > BO
2. AO < BO
3. AO â‰¤ BO
4. AO = BO
5. AO = BO/2
Solution

Since  is in slope-intercept form, we know the slope of the line is 9/10.

Now, the ratio of BO to AO is the slope of the line (rise over run).

Hence, . Multiplying both sides of this equation by AO yields .

In other words, BO is 9/10 the length of AO. Hence, AO is longer.