# What is the slope intercept form of the line passing through (1,11)  with a slope of -13 ?

Jun 5, 2017

See a solution process below:

#### Explanation:

The slope-intercept form of a linear equation is: $y = \textcolor{red}{m} x + \textcolor{b l u e}{b}$

Where $\textcolor{red}{m}$ is the slope and $\textcolor{b l u e}{b}$ is the y-intercept value.

We can substitute the slope given in the problem for $\textcolor{red}{m}$ and the values of the point given in the problem for $x$ and $y$ and solve for $\textcolor{b l u e}{b}$

$11 = \left(\textcolor{red}{- 13} \times 1\right) + \textcolor{b l u e}{b}$

$11 = - 13 + \textcolor{b l u e}{b}$

$\textcolor{red}{13} + 11 = \textcolor{red}{13} - 13 + \textcolor{b l u e}{b}$

$24 = 0 + \textcolor{b l u e}{b}$

$24 = \textcolor{b l u e}{b}$

$\textcolor{b l u e}{b} = 24$

We can now substitute the slope from the problem and the value of $b$ we calculated to write the equation:

$y = \textcolor{red}{- 13} x + \textcolor{b l u e}{24}$