# How do you write the equation of a line in point slope form and slope intercept form given Point: (1, –7); Slope: -2/3?

May 2, 2015

Point-slope form is $y + 7 = - \frac{2}{3} \left(x - 1\right)$ .

y-intercept form is $y = - \frac{2}{3} x + - \frac{19}{3}$ .

Point-slope form.

Slope, $m$, = $- \frac{2}{3}$.

Point=$\left(1 , - 7\right) = {x}_{1}$ and ${y}_{1}$.

Point-slope formula.

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

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

$y - \left(- 7\right) = - \frac{2}{3} \left(x - 1\right)$ =

$y + 7 = - \frac{2}{3} \left(x - 1\right)$

y-intercept form.

Slope, $m = - \frac{2}{3}$, $y = - 7$, $x = 1$.

y-intercept formula.

$y = m x + b$ =

Substitute the values for $y$, $x$, and $m$. Solve for slope-intercept, $b$.

$- 7 = - \frac{2}{3} \left(1\right) + b$ =

$- 7 = - \frac{2}{3} + b$ =

Flip the equation (optional).

$b - \frac{2}{3} = - 7$ =

$b = - 7 + \frac{2}{3}$ =

Make the denominators the same.

$b = - 7 \cdot \frac{3}{3} + \frac{2}{3}$ =

$b = - \frac{21}{3} + \frac{2}{3}$ =

$b = - \frac{19}{3}$

Now we can write the equation of the line in slope-intercept form.

$y = - \frac{2}{3} x + - \frac{19}{3}$