Observing the given graph, we can see that the line passes through the points $J (- 2, 3)$ and $K (3, - 2) .$ 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

- 5 .

Similarly, the

run,

or change in

x,

is

5 .

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

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 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{- 5}{5}

MoveNegNumToFrac

Put minus sign in front of fraction

m = - \frac{5}{5}

QuotOne

$\frac{a}{a} = 1$

m = - 1

A slope of

m = - 1

means that for every

1

step in the positive horizontal direction, the graph travels

1

step in the negative vertical direction.

Exercise