# How do you write an equation of a line with point (7,1), slope 8?

Feb 7, 2017

See the entire solution process below:

#### Explanation:

We can use the point-slope formula to write an equation for this line. The point-slope formula states: $\left(y - \textcolor{red}{{y}_{1}}\right) = \textcolor{b l u e}{m} \left(x - \textcolor{red}{{x}_{1}}\right)$

Where $\textcolor{b l u e}{m}$ is the slope and $\textcolor{red}{\left(\left({x}_{1} , {y}_{1}\right)\right)}$ is a point the line passes through.

We can substitute the slope and values from the point to give:

$\left(y - \textcolor{red}{1}\right) = \textcolor{b l u e}{8} \left(x - \textcolor{red}{7}\right)$

We can also transform this equation to the slope-intercept form by solving for $y$. 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.

$y - \textcolor{red}{1} = \left(\textcolor{b l u e}{8} \times x\right) - \left(\textcolor{b l u e}{8} \times \textcolor{red}{7}\right)$

$y - \textcolor{red}{1} = 8 x - 56$

$y - \textcolor{red}{1} + 1 = 8 x - 56 + 1$

$y - 0 = 8 x - 55$

$y = \textcolor{red}{8} x - \textcolor{b l u e}{55}$