# What is the equation of the line passing through (9,-2) with slope m= 2/3?

Mar 9, 2018

$2 x - 3 y - 24 = 0$

#### Explanation:

The equation of a line passing through two points $\left({x}_{1} , {y}_{1}\right)$ and having a slope $m$ is given by

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

Given: ${x}_{1} = 9 , {y}_{1} = \left(- 2\right) , m = \frac{2}{3}$

Therefore, equation of the line is
$\left(y - {y}_{1}\right) = m \left(x - {x}_{1}\right)$
$y - \left(- 2\right) = \frac{2}{3} \left(x - 9\right)$
$y + 2 = \frac{2}{3} \left(x - 9\right)$

Multiplying both sides by 3,
$3 y + 6 = 2 x - 18$
$2 x - 3 y - 24 = 0$

Mar 9, 2018

See explanation.

#### Explanation:

The slope of the line is given, so the equation is: $y = \frac{2}{3} x + b$.
All we have to do is to calculate the value of $b$ for which the given point lies on the line. To do this we have to substitute the coordinates of the point as $x$ and $y$:

## $- 2 = \frac{2}{3} \cdot 9 + b$

If we solve it we get:

$- 2 = 6 + b \implies b = - 8$

Finally we can answer the question:

The line equation is: $y = \frac{2}{3} x - 8$.