Observing the given graph, we can see that the line passes through the points $(- 2, 3)$ and $(3, 2) .$ We can use a graph to find the slope of a line. Let's take a look at the change in $x$ and $y$ between the given points.

We can see that as the line falls from left to right. Therefore, the slope is negative. The

rise,

or change in

y,

is

- 1 .

Similarly, the

run,

or change in

x,

is

5 .

Now we are ready to find the slope

m .

m = \frac{rise}{run} \Leftrightarrow m = \frac{- 1}{5} = - \frac{1}{5}

We can confirm this answer by using the formula.

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

We can use the given points to solve for the slope.

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

SubstitutePoints

Substitute $(- 2, 3)$ & $(3, 2)$

m = \frac{2 - 3}{3 - ( - 2 )}

SubNeg

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

m = \frac{2 - 3}{3 + 2}

AddSubTerms

Add and subtract terms

m = \frac{- 1}{5}

MoveNegNumToFrac

Put minus sign in front of fraction

m = - \frac{1}{5}

We got the same number as before. We can be sure the slope of the line is

- \frac{1}{5} .

Exercise 1 Page 149

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