# How do you write a equation in slope intercept form of the line passing through the given points (0,7) , (1,9)?

Jun 15, 2017

$y = 2 x + 7$

#### Explanation:

Given
$\textcolor{w h i t e}{\text{XXX}} \left({x}_{1} , {y}_{1}\right) = \left(0 , 7\right)$ and
$\textcolor{w h i t e}{\text{XXX}} \left({x}_{2} , {y}_{2}\right) = \left(1 , 9\right)$

The (y) intercept is the value of $y$ when $x = 0$
$\textcolor{w h i t e}{\text{XXX}}$given the point $\left({x}_{1.} , {y}_{1}\right) = \left(0 , 7\right)$
$\textcolor{w h i t e}{\text{XXX}}$the (y)intercept is $b = 7$

The slope of a line between two points is
$\textcolor{w h i t e}{\text{XXX}} m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$
$\textcolor{w h i t e}{\text{XXX}}$for the given points (above), the slope is
$\textcolor{w h i t e}{\text{XXX}} m = \frac{9 - 7}{1 - 0} = 2$

The slope-intercept form for a line with slope $m$ and (y) intercept $b$ is
$\textcolor{w h i t e}{\text{XXX}} y = m x + b$
$\textcolor{w h i t e}{\text{XXX}}$using the values we have just determined for $m$ and $b$
$\textcolor{w h i t e}{\text{XXX}} y = 2 x + 7$