b Can you find f(3) by looking at the graph? How would you find it using the equation?
C
c At what value for x has the climber reached 500 feet?
A
aSlope: 125
y-intercept: 50 Interpretation: See solution.
B
b f(3)=425
Interpretation: See solution.
C
c 3.6 hours, see solution.
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 of 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(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.
