Exercise 12 Page 169

a Let's look at the given graph.

Remember the slope-intercept form of a linear equation.

y = m x + b

In this form

m

is the slope and

b

is the

y -

intercept. We can write the equation in the graph in this form.

f (x) = 125 x + 50

We can see that

m = 125

is the slope and

b = 50

is the

y -

intercept. The slope tells us that the climber goes up

125

feet in elevation every hour. The

y -

intercept being

50

tells us that when the climber started climbing they were at an elevation of

50 feet .

b We can find

f (3)

by looking at the graph or algebraically by substituting

3

for

x

in the equation. Since the graph goes up by

0.4

on the

x -

axis, it is not easy to find the correct

x -

value, let alone the exact corresponding

y -

value. Solving algebraically is going to be easier and more accurate.

f (x) = 125 x + 50

Substitute

$x = 3$

f (3) = 125 \cdot 3 + 50

Multiply

f (3) = 375 + 50

AddTerms

Add terms

f (3) = 425

f (3) = 425

tells us that after

3

hours have passed, the climber will be at an elevation of

425

feet.

c Once again, we could solve this either graphically or algebraically. In this case, however, graphically is going to be easier. Doing it algebraically would require us to substitute

f (x) = 500

and solve for

x .

500 = 125 x + 50

When looking at the graph, though,

y = 500

feet lies perfectly on an intersection of graph lines. We can follow the line down to the

x -

axis from the point marking the end of his climb. This gives us that it took

x = 3.6

hours for the climber to reach the top.

Subchapter links

Exercises p.169