# What is the equation of the line with slope  m= -8/3  that passes through  (-17/15,-15/24) ?

Jun 9, 2017

See a 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 $\left(\textcolor{red}{{x}_{1} , {y}_{1}}\right)$ is a point the line passes through.

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

$\left(y - \textcolor{red}{- \frac{15}{24}}\right) = \textcolor{b l u e}{- \frac{8}{3}} \left(x - \textcolor{red}{- \frac{17}{15}}\right)$

$\left(y + \textcolor{red}{\frac{15}{24}}\right) = \textcolor{b l u e}{- \frac{8}{3}} \left(x + \textcolor{red}{\frac{17}{15}}\right)$

We can also solve this equation for $y$ to transform it to 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.

$y + \textcolor{red}{\frac{15}{24}} = \left(\textcolor{b l u e}{- \frac{8}{3}} \times x\right) + \left(\textcolor{b l u e}{- \frac{8}{3}} \times \textcolor{red}{\frac{17}{15}}\right)$

$y + \textcolor{red}{\frac{15}{24}} = - \frac{8}{3} x - \frac{136}{45}$

$y + \textcolor{red}{\frac{15}{24}} - \frac{15}{247} = - \frac{8}{3} x - \frac{136}{45} - \frac{15}{24}$

$y + 0 = - \frac{8}{3} x - \left(\frac{24}{24} \times \frac{136}{45}\right) - \left(\frac{45}{45} \times \frac{15}{24}\right)$

$y = - \frac{8}{3} x - \left(\frac{3264}{1080}\right) - \left(\frac{675}{1080}\right)$

$y = - \frac{8}{3} x - \frac{3939}{1080}$

$y = - \frac{8}{3} x - \frac{3 \times 1313}{3 \times 360}$

$y = - \frac{8}{3} x - \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} \times 1313}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} \times 360}$

$y = - \frac{8}{3} x - \frac{1313}{360}$