Understand Slope of a Line: example 11.38

Find the slope of the line between the points $(1, 2)$ and $(4, 5) .$

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 given points: $(8, 5)$ and $(6, 3) .$

How did it go?

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

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