# How do you find an equation of the line having the given slope m=6/7 and containing the given point (6, -6)?

Jul 2, 2017

See a solution process below:

#### Explanation:

We can use the point-slope formula to write and 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 $\left(\textcolor{red}{{x}_{1} , {y}_{1}}\right)$ is a point the line passes through.

Substituting the slope and values from the point in the problem gives:

$\left(y - \textcolor{red}{- 6}\right) = \textcolor{b l u e}{\frac{6}{7}} \left(x - \textcolor{red}{6}\right)$

$\left(y + \textcolor{red}{6}\right) = \textcolor{b l u e}{\frac{6}{7}} \left(x - \textcolor{red}{6}\right)$

If necessary, we can solve for $y$ to put the equation in slope-intercept form. 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.

$y + \textcolor{red}{6} = \left(\textcolor{b l u e}{\frac{6}{7}} \cdot x\right) - \left(\textcolor{b l u e}{\frac{6}{7}} \cdot \textcolor{red}{6}\right)$

$y + \textcolor{red}{6} = \frac{6}{7} x - \frac{36}{7}$

$y + \textcolor{red}{6} - 6 = \frac{6}{7} x - \frac{36}{7} - 6$

$y + 0 = \frac{6}{7} x - \frac{36}{7} - \left(\frac{7}{7} \times 6\right)$

$y = \frac{6}{7} x - \frac{36}{7} - \frac{42}{7}$

$y = \textcolor{red}{\frac{6}{7}} x - \textcolor{b l u e}{\frac{78}{7}}$