Understand Slope of a Line: example 11.39

Find the slope of the line through the points $(−2, −3)$ and $(−7, 4) .$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Find the slope of the line through the pair of points: $(−3, 4)$ and $(2, −1) .$

How did it go?

We’ll call $(−2, −3)$ point #1 and $(−7, 4)$ point #2.	$\overset{x_{1}, y_{1}}{(−2, −3)} and \overset{x_{2}, y_{2}}{(−7, 4)}$
Use the slope formula.	$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$
Substitute the values
$y$ of the second point minus $y$ of the first point	$m = \frac{4 - (−3)}{x_{2} - x_{1}}$
$x$ of the second point minus $x$ of the first point	$m = \frac{4 - (−3)}{−7 - (−2)}$
Simplify.	$m = \frac{7}{−5}$
	$m = - \frac{7}{5}$

We’ll call $(−2, −3)$ point #1 and $(−7, 4)$ point #2.	$\overset{x_{1}, y_{1}}{(−2, −3)} and \overset{x_{2}, y_{2}}{(−7, 4)}$
Use the slope formula.	$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$
Substitute the values
$y$ of the second point minus $y$ of the first point	$m = \frac{4 - (−3)}{x_{2} - x_{1}}$
$x$ of the second point minus $x$ of the first point	$m = \frac{4 - (−3)}{−7 - (−2)}$
Simplify.	$m = \frac{7}{−5}$
	$m = - \frac{7}{5}$