# How do you determine the slope of the line passing through (2, 3) and (4, 7)?

May 3, 2018

$2$

#### Explanation:

To find the slope of a line, use the slope formula:

$\text{slope" = "change in y"/"change in x}$

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

I will call $\left(2 , 3\right)$ Point 1, so:
${x}_{1} = 2$
${y}_{1} = 3$

I will call $\left(4 , 7\right)$ Point 2, so:
${x}_{2} = 4$
${y}_{2} = 7$

Now substitute those values into the slope formula and simplify:

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

$m = \frac{7 - 3}{4 - 2}$

$m = \frac{4}{2}$

$m = 2$

The slope of a line passing through $\left(2 , 3\right)$ and $\left(4 , 7\right)$ is $2$:

As you can see if I graph this line, the slope is $2$:
graph{y=2x -1 [-10, 10, -5, 5]}