# What is the slope of the line that runs through points (1,-5) and (5, 10)?

May 14, 2017

See a solution process below:

#### Explanation:

The slope can be found by using the formula: $m = \frac{\textcolor{red}{{y}_{2}} - \textcolor{b l u e}{{y}_{1}}}{\textcolor{red}{{x}_{2}} - \textcolor{b l u e}{{x}_{1}}}$

Where $m$ is the slope and ($\textcolor{b l u e}{{x}_{1} , {y}_{1}}$) and ($\textcolor{red}{{x}_{2} , {y}_{2}}$) are the two points on the line.

Substituting the values from the points in the problem gives:

$m = \frac{\textcolor{red}{10} - \textcolor{b l u e}{- 5}}{\textcolor{red}{5} - \textcolor{b l u e}{1}} = \frac{\textcolor{red}{10} + \textcolor{b l u e}{5}}{\textcolor{red}{5} - \textcolor{b l u e}{1}} = \frac{15}{4}$

May 14, 2017

$\frac{5}{3}$

#### Explanation:

To find the slope, we need to use the, creatively named, Point-Slope Formula, which uses, wait for it, two points to find the slope

The form is $\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$, based on $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$.

So, we have $\left(1 , - 5\right)$ and $\left(5 , 10\right)$. That gives us $\frac{10 - - 5}{10 - 1}$, or $\frac{15}{9}$, which simplifies to $\frac{5 \cdot \cancel{3}}{3 \cdot \cancel{3}}$: $\frac{5}{3}$. That's our slope