# What is the equation of a line that has an x-intercept of -2 and a y-intercept of -5?

Jun 10, 2018

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

#### Explanation:

$\text{the equation of a line in "color(blue)"slope-intercept form}$ is.

•color(white)(x)y=mx+b

$\text{where m is the slope and b the y-intercept}$

$\text{here } b = - 5$

$y = m x - 5 \leftarrow \textcolor{b l u e}{\text{is the partial equation}}$

$\text{to calculate m use the "color(blue)"gradient formula}$

•color(white)(x)m=(y_2-y_1)/(x_2-x_1)

$\text{let "(x_1,y_1)=(-2,0)" and } \left({x}_{2} , {y}_{2}\right) = \left(0 , - 5\right)$

$m = \frac{- 5 - 0}{0 - \left(- 2\right)} = \frac{- 5}{2} = - \frac{5}{2}$

$y = - \frac{5}{2} x - 5 \leftarrow \textcolor{red}{\text{ is the equation of the line}}$

Jun 10, 2018

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

#### Explanation:

You have 2 points on the line:

$\left(- 2 , 0\right) , \left(0 - 5\right)$

Use slope point formula

First you determine the slope:

$\left(\textcolor{b l u e}{{x}_{1}} , \textcolor{b l u e}{{y}_{1}}\right) = \left(- 2 , 0\right)$

$\left(\textcolor{red}{{x}_{2}} , \textcolor{red}{{y}_{2}}\right) = \left(0 , - 5\right)$

$\textcolor{g r e e n}{m} = \frac{\textcolor{red}{{y}_{2}} - \textcolor{b l u e}{{y}_{1}}}{\textcolor{red}{{x}_{2}} - \textcolor{b l u e}{{x}_{1}}}$

$\textcolor{g r e e n}{m} = \frac{\textcolor{red}{- 5} - \textcolor{b l u e}{0}}{\textcolor{red}{0} - \textcolor{b l u e}{\left(- 2\right)}} = - \frac{5}{2}$

Now use the Point Slope form of a line:

$\left(y - \textcolor{b l u e}{{y}_{1}}\right) = \textcolor{g r e e n}{m} \left(x - \textcolor{b l u e}{{x}_{1}}\right)$

$\left(y - \textcolor{b l u e}{\left(- 5\right)}\right) = \textcolor{g r e e n}{- \frac{5}{2}} \left(x - \textcolor{b l u e}{0}\right)$

$y + 5 = - \frac{5}{2} x$

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

graph{y=-5/2x - 5 [-10, 10, -5, 5]}