Exercise 12 Page 169

Practice makes perfect

a Let's look at the given graph.

Remember the slope-intercept form of a linear equation. y = mx + 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)= 125x+ 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 50feet.

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)=125x+50

Substitute

x= 3

f( 3)=125* 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=125x+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.

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