Question

How do you find a standard form equation for the line with `(-4,2)` and `(6,8)`?

Answer 1

The equation is `-3x+5y=22`

Explanation:

Standard form of an equation: ax+by=c (a, b, and c must be integers)

To find the standard form, first I'll find and write the equation in slope-intercept form.
Slope-intercept form of an equation: y=mx+b, where m is the slope of the line and b is the y-intercept

To find the slope through two points, divide the difference of the y-coordinates by the difference of the x-coordinates

`(y_2-y_1)/(x_2-x_1)`

`(8-2)/(6-(-4))`

`6/10`

`3/5 rarr` This is the simplified slope

So far, the equation is `y=3/5x+b`

To find b, let's plug in one of the points

`8=3/5*6+b`

`8=18/5+b`

`8=3 3/5+b`

`b=4 2/5`

The equation is `y=3/5x+4 2/5` (in slope-intercept form)

`y-3/5x=4 2/5`

`-3/5x+y=4 2/5 rarr` We still have to get rid of the denominators

`-3x+5y=22 rarr` Multiply the equation by 5