# What is the equation of the line with slope  m= -5  that passes through  (-13,-7) ?

May 29, 2018

$y = - 5 x - 72$

#### Explanation:

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

•color(white)(x)y=mx+b

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

$\text{here } m = - 5$

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

$\text{to find b substitute "(-13,-7)" into }$
$\text{the partial equation}$

$- 7 = 65 + b \Rightarrow b = - 7 - 65 = - 72$

$y = - 5 x - 72 \leftarrow \textcolor{red}{\text{is the equation of line}}$

May 29, 2018

$y = - 5 x + b$

#### Explanation:

Equation of line in slope format is $y = m x + b$, where $m$ is the slope of the line and $b$ is y-intercept.

Hence from the given data, the equation of the line is:

$y = - 5 x + b$

Now, we can calculate the value of $b$ from points $\left(- 13 , - 7\right)$.

$y = - 5 x + b$

$- 7 = - 5 \left(- 13\right) + b$

$- 7 = 65 + b$

$- 7 - 65 = b$

$b = - 72$

Therefore equation of line in slope format is $y = - 5 x + b$