# What is the equation of the line with slope  m= -11/3  that passes through  (13/15,-23/24) ?

Mar 15, 2016

$y = - \frac{11}{3} x + \frac{799}{360}$

#### Explanation:

Recall that the general equation of a line is:

$\textcolor{b l u e}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} y = m x + b \textcolor{w h i t e}{\frac{a}{a}} |}}}$

where:
$y =$y-coordinate
$m =$slope
$x =$x-coordinate
$b =$y-intercept

Determining the Equation
$1$. Start by substituting $\textcolor{\mathmr{and} a n \ge}{m = - \frac{11}{3}}$ into the formula.

$y = m x + b$

$y = \textcolor{\mathmr{and} a n \ge}{- \frac{11}{3}} x + b$

$2$. Since you are also given the coordinate, $\left(\textcolor{p u r p \le}{\frac{13}{15}} , \textcolor{t e a l}{- \frac{23}{24}}\right)$, substitute it into the equation as well.

$\textcolor{t e a l}{- \frac{23}{24}} = \textcolor{\mathmr{and} a n \ge}{- \frac{11}{3}} \textcolor{p u r p \le}{\left(\frac{13}{15}\right)} + b$

$3$. Solve for the unknown value of the variable, $b$.

$- \frac{23}{24} = - \frac{143}{45} + b$

$b = \frac{799}{360}$

$4$. Rewrite the equation.

$\textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} y = - \frac{11}{3} x + \frac{799}{360} \textcolor{w h i t e}{\frac{a}{a}} |}}}$