# How do you write an equation in slope intercept form given (5,7), (-3,11)?

Nov 14, 2016

$y = - 12 x + 9 \frac{1}{2}$

#### Explanation:

Step 1: Write in slope-point form

$\textcolor{w h i t e}{\text{XXX}}$Step 1a: Determine the slope
$\textcolor{w h i t e}{\text{XXX}} \textcolor{g r e e n}{m} = \frac{\Delta y}{\Delta x} = \frac{11 - 7}{- 3 - 5} = \frac{4}{- 8} = \textcolor{g r e e n}{- \frac{1}{2}}$

$\textcolor{w h i t e}{\text{XXX}}$Step 1b: Use one of the given points to write in slope-point form:
$\textcolor{w h i t e}{\text{XXX}} y - 7 = - \frac{1}{2} \left(x - 5\right)$

Step 2: Convert into slope-intercept form:
$\textcolor{w h i t e}{\text{XXX}}$Note the slope-intercept form is
$\textcolor{w h i t e}{\text{XXXXXX}} y = \textcolor{g r e e n}{m} x + \textcolor{b l u e}{b}$
$\textcolor{w h i t e}{\text{XXX}}$for a line with slope $\textcolor{g r e e n}{m}$ and y-intercept $\textcolor{b l u e}{b}$

$\textcolor{w h i t e}{\text{XXX}} y = \textcolor{g r e e n}{- \frac{1}{2}} x + \frac{5}{2} + 7$

$\textcolor{w h i t e}{\text{XXX}} y = \textcolor{g r e e n}{- \frac{1}{2}} x + \textcolor{b l u e}{\frac{19}{2}}$

Here is the graph of $y = - \frac{1}{2} x + \frac{19}{2}$ with the given points for verification purposes: 