# How do you write an equation in slope intercept form for the line parallel to : y=5x-2 that passes through (8, -2)?

Oct 7, 2015

$y = 5 x + \left(- 42\right)$

#### Explanation:

y=5x-2 (=color(red)(5)x+(color(blue)(-2))
has a slope of $\textcolor{red}{m} = \textcolor{red}{5}$

Any line parallel to $y = 5 x - 2$ will have the same slope.
That is any line parallel to $y = 5 x - 2$ has a slope of $5$

If such a line passes through $\left(8 , - 2\right)$ then
$\textcolor{w h i t e}{\text{XXX}} \frac{\Delta y}{\Delta x} = \frac{y - \left(- 2\right)}{x - 8} = 5$

$\rightarrow \textcolor{w h i t e}{\text{XXX}} y + 2 = 5 x - 40$

$\rightarrow \textcolor{w h i t e}{\text{XXX}} y = 5 x - 42$
which is slope-intercept form with a slope of $5$ and a y-intercept of $\left(- 42\right)$