What is the equation of the line with slope  m= -9/5  that passes through  (-10,23) ?

Jan 1, 2016

Point-slope form: $y - 23 = - \frac{9}{5} \left(x + 10\right)$

Slope-intercept form: $y = - \frac{9}{5} + 5$

Explanation:

Point-Slope Form
When you have the slope and one point on a line, you can use the point-slope form to find the equation for the line. The general equation is $y - {y}_{1} = m \left(x - {x}_{1}\right)$, where $m = - \frac{9}{5}$ and $\left({x}_{1} , {y}_{1}\right)$ is $\left(- 10 , 23\right)$.

Substitute the given values into the point-slope equation.

y-23=-9/5(x-(-10)

Simplify.

$y - 23 = - \frac{9}{5} \left(x + 10\right)$

Converting to Slope-Intercept Form
If desired, you can convert from point-slope form to slope-intercept form by solving for $y$. The general form is $y = m x + b$, where $m$ is the slope, and $b$ is the y-intercept.

$y - 23 = - \frac{9}{5} \left(x + 10\right)$

Add $23$ to both sides.

$y = - \frac{9}{5} \left(x + 10\right) + 23$

Distribute $- \frac{9}{5}$.

$y = - \frac{9}{5} x - \frac{90}{5} + 23$

Simplify $- \frac{90}{5}$ to $- 18$.

$y = - \frac{9}{5} x - 18 + 23$

Simplify.

$y = - \frac{9}{5} + 5$, where $m = - \frac{9}{5}$ and $b = 5$.

graph{y=-9/5x+5 [-10.08, 9.92, -2.84, 7.16]}