# What is the equation of the line that has a slope of 2 and goes through (1,5)?

Mar 10, 2018

$y = 2 x + 3$

#### Explanation:

Use the point-slope formula:

$y - {y}_{1} = m \left(x - {x}_{1}\right)$

Where:

$\left({x}_{1} , {y}_{1}\right)$ is a point on the graph

$m$ is the slope

From the information given to us,

$\left({x}_{1} , {y}_{1}\right) \to \left(1 , 5\right)$

$m = 2$

So...

$y - {y}_{1} = m \left(x - {x}_{1}\right)$
$\text{ } \downarrow$
$y - \left(5\right) = 2 \left(x - \left(1\right)\right)$

To get into $y = m x + b$ form, all we do is solve for $y$

$y - \left(5\right) = 2 \left(x - \left(1\right)\right)$

$y - 5 = 2 x - 2$

$y - 5 + 5 = 2 x - 2 + 5$

$y = 2 x + 3$

The graph of this is shown below:

graph{2x+3 [-10, 10, -5, 5]}