# How do you find the slope of the line passing through the points (-7,3) and (3,8)?

Mar 26, 2018

$\frac{1}{2}$

#### Explanation:

$m = \frac{{y}_{1} - {y}_{2}}{{x}_{1} - {x}_{2}} \mathmr{and} \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$
${p}_{1} \left(- 7 , 3\right)$
${p}_{2} \left(3 , 8\right)$
$m = \frac{3 - 8}{- 7 - 3} = \frac{- 5}{- 10} = \frac{1}{2}$

Mar 26, 2018

Need to find the change in $x$ and $y$
$\Delta x = 3 - - 7 = 10$
$\Delta y = 8 - 3 = 5$

We know that slopes and gradients are merely just the rise over the run or the change in y over the change in x $\frac{\Delta y}{\Delta x} = \frac{5}{10} = \frac{1}{2}$

Mar 26, 2018

1/2

#### Explanation:

$m = \left({y}_{\text{2"-y_"1")/(x_"2"-x_"1}}\right)$

$m = \frac{3 - 8}{- 7 - 3} = \frac{- 5}{-} 10 = \frac{1}{2}$

Mar 26, 2018

The slope is $\frac{1}{2}$

#### Explanation:

Slope is defined as the change in y over x- $\frac{\Delta y}{\Delta x}$, or as my math teacher always said:

"The rise over the run"

(You rise vertically=(y-direction) and run horizontally= (x-direction)

This can be written as:

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

Then we just plug in your two points x and y values (which point you decide to allocate to 1 or 2 does not matter)

Slope=$\frac{8 - 3}{\left(3\right) - \left(- 7\right)} = \left(\frac{5}{10}\right) = \left(\frac{1}{2}\right)$