# Find an equation of the line described below. Write the equation in​ slope-inter

Find an equation of the line described below. Write the equation in​ slope-intercept form​ (solved for​ y), when possible.
Through
​(8​,4​) and (4​,8​)
What is the equation of the​ line?
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Elberte
Step 1
Given, the line passing through (8​,4​) and (4​,8​)
Step 2
Suppose
$\left({x}_{1},{y}_{1}\right)=\left(8,4\right)$
$\left({x}_{2},{y}_{2}\right)=\left(4,8\right)$
The slope is
$m=\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}$
$=\frac{8-4}{4-8}$
$=\frac{4}{-4}$
=-1
The equation of the line passing through $\left({x}_{1},{y}_{1}\right)\left({x}_{1},{y}_{2}\right)$ with slope m is
$y-{y}_{1}=m\left(x-{x}_{1}\right)$
$⇒y-4=-1\left(x-8\right)$
$⇒y-4=-x+8$
$⇒y=-x+8+4$
$⇒y=-x+12$