# How do you write the equation of a line with m=5/6 and (7,-2)?

Dec 26, 2016

The equation is $y - {y}_{1} = m \left(x - {x}_{1}\right)$. Solve for $y$.

#### Explanation:

Use the point slope formula, $y - {y}_{1} = m \left(x - {x}_{1}\right)$, where $m$ is the slope, $\frac{5}{6}$, ${x}_{1}$ and ${y}_{1}$ are the point $\left(7 , - 2\right)$.

Substitute the known values into the equation.

$y - \left(- 2\right) = \frac{5}{6} \left(x - 7\right)$

Simplify.

$y + 2 = \frac{5}{6} x - \frac{35}{6}$

Subtract $2$ from both sides.

$y = \frac{5}{6} x - \frac{35}{6} - 2$

Convert $2$ into a fraction that has a denominator of $6$.

$y = \frac{5}{6} x - \frac{35}{6} - \left(\frac{2}{1} \times \frac{6}{6}\right)$

Simplify,

$y = \frac{5}{6} x - \frac{35}{6} - \frac{12}{6}$

Simplify,

$y = \frac{5}{6} x - \frac{47}{6}$