# What is the equation in point-slope form and slope intercept form for the line given slope= 8/3,(-2,-6)?

May 5, 2015

General point slope form :
$y - {y}_{1} = m \left(x - {x}_{1}\right)$
for a given slope $m$ and a point on the line $\left({x}_{1} , {y}_{1}\right)$

From the given data:
$y + 6 = \frac{8}{3} \left(x + 2\right)$

General slope-intercept form:
$y = m x + b$
for a given slope $m$ and a y-intercept $b$

From the given data
$y = \frac{8}{3} x + b$
but we still need to determine the value of $b$
If we insert the values of the point $\left(x , y\right) = \left(- 2 , - 6\right)$
$- 6 = \frac{8}{3} \left(- 2\right) + b$
$b = - 6 + \frac{16}{3} = - 6 + 5 \frac{1}{3} = - \frac{2}{3}$
and the slope-intercept form is
$y = \frac{8}{3} x - \frac{2}{3}$