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

Mar 24, 2018

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

#### 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

$\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

$\frac{8 - 2}{6 - \left(- 4\right)}$

$\frac{6}{10}$

$\frac{3}{5} \rightarrow$ This is the simplified slope

So far, the equation is $y = \frac{3}{5} x + b$

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

$8 = \frac{3}{5} \cdot 6 + b$

$8 = \frac{18}{5} + b$

$8 = 3 \frac{3}{5} + b$

$b = 4 \frac{2}{5}$

The equation is $y = \frac{3}{5} x + 4 \frac{2}{5}$ (in slope-intercept form)

$y - \frac{3}{5} x = 4 \frac{2}{5}$

$- \frac{3}{5} x + y = 4 \frac{2}{5} \rightarrow$ We still have to get rid of the denominators

$- 3 x + 5 y = 22 \rightarrow$ Multiply the equation by 5