# Linear equation

The linear equations of y=-x+5 and y=.5x+2. The x's are variables.

In mathematics, a linear equation is a type of equation. A linear equation is the equation of a straight line. This type of equation is written in the form:

${\displaystyle y=mx+b}$

or ${\displaystyle (y-y_{1})=m(x-x_{1})}$ also known as rise over run.

The m is the rate of change or slope.

The slope is how fast the line moves up or down. Numbers farther from 0, or a larger absolute value will make the slope steeper.

If m is a negative number, then the line will appear to fall or go down the page when read from left to right.

If m is a positive number, then the line will appear to climb the page when read from left to right.

While b is the y-intercept of the function.

This is where the function crosses the y-axis of the coordinate plane. The first equation is called slope-intercept form because, in it, the slope (m) and y-intercept (b) are easily found. The second equation is called point-slope form because, in it, a point on the graph (x1, y1) and the slope (m) are easily found.

You can find the slope of a graph by seeing how much the y-value increases by for every one x-value. You can find the y-intercept of a graph by looking at where the x coordinate equals 0, and see what the y-value equals.