# What is the equation of the line with slope  m= -1/4  that passes through  (7,3) ?

Feb 11, 2016

The equation of the line would be $y = - \frac{1}{4} x + \frac{19}{4}$

#### Explanation:

The formula for the slope intercept form is

$y = m x + b$

where $m$ is the slope and $b$ is the $y$-intercept. In this problem, you are given the slope or $m$. To find the $y$-intercept, you plug in the point that is given, $\left(7 , 3\right)$ into $x$ and $y$ respectively and solve for $b$.

$y = \left(- \frac{1}{4}\right) x + b$

$3 = \left(- \frac{1}{4}\right) \left(7\right) + b$

$3 = \left(- \frac{7}{4}\right) + b$

$\frac{12}{4} = \left(- \frac{7}{4}\right) + b$

Add $\left(\frac{7}{4}\right)$ to both sides

$b = \left(\frac{19}{4}\right)$

Plug b into the slope intercept equation

$y = - \frac{1}{4} x + \frac{19}{4}$