Question #eda1b

Oct 26, 2017

$y = - \frac{6}{5} x + \frac{23}{5}$

Explanation:

When dealing with linear equation problems. you should know these two forms:
standard form: $y = m x + b$
slope-intercept form: ${y}_{1} - {y}_{2} = m \left({x}_{1} - {x}_{2}\right)$

Standard form is when you're dealing with one point. Slope-intercept form deals with two points. The question said to get the answer into standard form, which means that we need a slope $m$ and slope-intercept $b$.

First, we will find the slope $m$ using the slope-intercept form.
$\left(- 2 , 7\right) , \left(3 , 1\right) = \left({x}_{2} , {y}_{2}\right) , \left({x}_{1} , {y}_{1}\right)$
${y}_{1} - {y}_{2} = m \left({x}_{1} - {x}_{2}\right)$
$1 - 7 = m \left(3 - \left(- 2\right)\right)$
$m = - \frac{6}{5} = s l o p e$

Now that we have our slope $m$, we can use the slope $m$ and any given point $\left(- 2 , 7\right) \mathmr{and} \left(3 , 1\right)$ to find our slope-intercept $b$.
$y = m x + b$
$1 = \left(- \frac{6}{5}\right) \cdot 3 + b$
$b = \frac{23}{5}$

Now that we have our slope $m$ and our slope-intercept $b$, we can find the equation of the line between the two points.
$y = m x + b$
$y = - \frac{6}{5} x + \frac{23}{5}$