# Understanding Line Equations

In coordinate geometry, there are different line equations you can use, depending on whether a line is horizontal, vertical, or at an angle, and whether you know the line’s y-intercept.

Here are the basic forms for equations of lines:

**Slope-intercept form.**Use this form when you know (or can easily find) a line’s slope and its*y-intercept*(the point where the line crosses the*y*-axis).

*y*=*mx*+*b,*where*m*is the slope and*b*is the*y-*intercept.**Point-slope form.**This is the easiest form to use when you don’t know a line’s*y*-intercept but you do know the coordinates of a point on the line; you also need to know the line’s slope.

*y*–*y*_{1}=*m*(*x*–*x*_{1}), where*m*is the slope and (*x*_{1},*y*_{1}) is a point on the line.**Horizontal line.**This form is used for lines with a slope of zero.

*y*=*b*, where*b*is the*y-*intercept.

The*b*(or the number that’s plugged into*b*) tells you how far up or down the line is along the*y*-axis. Note that every point along a horizontal line has the same*y*-coordinate, namely*b*. In case you’re curious, this equation form is a special case of*y*=*mx*+*b*, where*m*= 0.**Vertical line.**And here’s the equation for a line with an undefined slope.

*x*=*a*, where*a*is the*x*-intercept.

The*a*(or the number that’s plugged into*a*) tells you how far to the right or left the line is along the*x*-axis. Every point along a vertiscal line has the same*x*-coordinate, namely*a*.

Don’t mix up the equations for horizontal and vertical lines. This mistake is extremely common. Because a horizontal line is parallel to the x-axis, you might think that the equation of a horizontal line would be x = a. And you might figure that the equation for a vertical line would be y = b because a vertical line is parallel to the y-axis. But as you see in the preceding equations, it’s the other way around.