How do you find the "m" and "b" of any linear equation?

1 Answer
Mar 19, 2018

m is the slope, while b is the y-intercept.

Explanation:

Any linear equation has the form of

y=mx+b

  • m is the slope of the equation

  • b is the y-intercept

The slope of the line, m, is found by

m=(y_2-y_1)/(x_2-x_1)

where (x_1,y_1) and (x_2,y_2) are the coordinates of any two points in the line.

The y-intercept, b, is found by plugging in x=0 into the equation, which results in y=b, and therefore is the y-intercept.

In some cases, if the equation is already arranged for you nicely, like y=3x+5, we can easily find the y-intercept for this line, which is 5.

Other times, the equation might not be arranged nicely, with cases such as 1/2x+3y=5, in which we solve for the y-intercept:

1/2x+3y=4

3y=4-1/2x

y=(-1/2x+4)/3

y=-1/6x+4/3

So, the y-intercept of this line is 4/3.