Exercise 12 Page 193

Observing the given graph, we can see that the line passes through the points $C (- 2, - 1)$ and $D (5, 5) .$ One way to use a graph to find the slope of a line is to count out the change in $x$ and $y .$

We can see that as the graph travels from left to right, the

rise,

or change in

y,

is

6 .

Similarly, the

run,

or change in

x,

is

7 .

slope = \frac{rise}{run} \Leftrightarrow m = \frac{6}{7}

We can confirm this answer by using the other method, the Slope Formula.

m = \frac{y _{2} - y _{1}}{x _{2} - x _{1}}

We will use the given points to find the slope.

m = \frac{y _{2} - y _{1}}{x _{2} - x _{1}}

SubstitutePoints

Substitute $(- 2, - 1)$ & $(5, 5)$

m = \frac{5 - ( - 1 )}{5 - ( - 2 )}

SubNeg

$a - (- b) = a + b$

m = \frac{5 + 1}{5 + 2}

AddTerms

Add terms

m = \frac{6}{7}

A slope of

m = \frac{6}{7}

means that for every

7

steps in the positive horizontal direction, the graph travels

6

steps in the positive vertical direction.