# What is the equation in y=mx+b of the line through points (0,2) , (1,7)?

Jun 22, 2015

$y = 5 x + 2$

#### Explanation:

Given the points $\left(0 , 2\right)$ and $\left(1 , 7\right)$
the slope is
$\textcolor{w h i t e}{\text{XXXX}}$$m = \frac{\Delta y}{\Delta x} = \frac{7 - 2}{1 - 0} = 5$

For any point $\left(x , y\right)$ (combined with $\left(0 , 2\right)$) on this line the slope is
$\textcolor{w h i t e}{\text{XXXX}}$$m = \frac{\Delta y}{\Delta x} = \frac{y - 2}{x - 0}$

So
$\textcolor{w h i t e}{\text{XXXX}}$$\frac{y - 2}{x - 0} = 5$
or
$\textcolor{w h i t e}{\text{XXXX}}$$y - 2 = 5 x$

In slope y-intercept form ($y = m x + b$) this becomes
$\textcolor{w h i t e}{\text{XXXX}}$$y = 5 x + 2$