Question

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

Answer 1

`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`.