Exercise 6 Page 141

Observing the given graph, we can see that the line passes through the points (1,-1) and (4,3). 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 4. Similarly, the run, or change in x, is 3. slope=rise/run ⇔ m=4/3 We can confirm this answer by using the other method, the Slope Formula. m = y_2-y_1/x_2-x_1 We will use the given points to solve for the slope.

m = y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( 1,-1) & ( 4,3)

m=3-( -1)/4- 1

SubNeg

a-(- b)=a+b

m=3+1/4-1

AddSubTerms

Add and subtract terms

m=4/3

A slope of m= 43 means that for every 3 steps in the positive horizontal direction, the graph travels 4 steps in the positive vertical direction.