# What is the slope of a line that passes through (-2, -3) and (1, 1)?

Jun 16, 2018

See a solution process below:

#### Explanation:

The formula for find the slope of a line is:

$m = \frac{\textcolor{red}{{y}_{2}} - \textcolor{b l u e}{{y}_{1}}}{\textcolor{red}{{x}_{2}} - \textcolor{b l u e}{{x}_{1}}}$

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

Substituting the values from the points in the problem gives:

$m = \frac{\textcolor{red}{1} - \textcolor{b l u e}{- 3}}{\textcolor{red}{1} - \textcolor{b l u e}{- 2}} = \frac{\textcolor{red}{1} + \textcolor{b l u e}{3}}{\textcolor{red}{1} + \textcolor{b l u e}{2}} = \frac{4}{3}$

Jun 16, 2018

Slope: $\frac{4}{3}$

#### Explanation:

The slope of a line between two points color(blue)(""(x_1,y_1)) and color(green)(""(x_2,y_2))
is the difference between the $y$ coordinate values divided by the difference between the $x$ coordinate values (taken in the same order);
that is
color(white)("XXX")"slope" = (color(green)(y_2)-color(blue)(y_1))/(color(green)(x_2)-color(blue)(x_1))

In this case we have the points color(blue)(""(-2,-3)) and color(green)(""(1,1)) (notice that the order of listing these does not matter)
So
color(white)("XXX")"slope"=(color(green)1-color(blue)(""(-3)))/(color(green)1-color(blue)(""(-2)))=4/3