## Line Equation

**Point-slope and Slope-intercept forms of a line**

These are two common formulations for the equation for a line.

__form of a line is:__

Slope-intercept

Slope-intercept

y=mx+b

It is useful if you want to know the slope, m, and, well, the y-intercept of the line, b. Conversely, you can find the equation for this line if you know the slope and y-intercept.

__Point-slope__form of a line is:

y-y1=m(x-x1)

where (x1,y1) is a point on the line.

This version of the equation for a line is useful if you know the slope of the line, and a point on the line, or conversely, you can derive this equation if you know slope and a point.

How to derive Point-slope:

slope is defined as rise over run, or change in y divided by change in x

slope = m =

__change in y__=

__y-y1__

change in x x-x1

So you get

m =

__y-y1__

x-x1

If you multiply both sides by (x-x1), you end up with the point-slope formula for a line:

y-y1 = m(x-x1)

Note that you can convert between the two forms.

Point-slope to slope intercept: just solve for y, and simplify the other side.

y-y1 = m(x-x1)

y=y1+ m(x-x1)

y=y1+ mx -mx1

y=mx +(y1-mx1)

y=mx + b

So that the y-intercept is y1-mx1.

To go from slope-intercept to point-slope, just plug in a number for x, and find the corresponding y value. Plug these in for x1 and y1, and use the point-slope formula.