What is the equation of the line with slope  m= -1/4  that passes through  (7,13) ?

Nov 15, 2015

$y = - \frac{1}{4} x + \frac{59}{4}$

Explanation:

Make use of the point-slope form $y - {y}_{1} = m \left(x - {x}_{1}\right)$ where $m$ is the slope and ${x}_{1}$ and ${y}_{1}$ are the $x$ and $y$ values of the given point.

$\left[1\right] \text{ } y - {y}_{1} = m \left(x - {x}_{1}\right)$

Substitute the values of $m$, ${x}_{1}$, and ${y}_{1}$.

$\left[2\right] \text{ } y - \left(13\right) = \left(- \frac{1}{4}\right) \left[x - \left(7\right)\right]$

Distribute $- \frac{1}{4}$ to $\left(x - 7\right)$.

$\left[3\right] \text{ } y - 13 = - \frac{1}{4} x + \frac{7}{4}$

Add $13$ to both sides.

$\left[4\right] \text{ } y - 13 + 13 = - \frac{1}{4} x + \frac{7}{4} + 13$

$\left[5\right] \text{ } y = - \frac{1}{4} x + \frac{7}{4} + 13$

Add $\frac{7}{4}$ and $13$.

$\left[6\right] \text{ } y = - \frac{1}{4} x + \frac{7}{4} + \frac{52}{4}$

$\left[7\right] \text{ } \textcolor{b l u e}{y = - \frac{1}{4} x + \frac{59}{4}}$