Q:

a group of hikers park there trail head and hike into the forest to a campsite. The next morning they head out on a hike from their campsite walking at a steady rate. The graph shows their distance in miles d from the car on the day of their hike after h hours. How many miles will the campers be from their car after 12 hours?

Accepted Solution

A:
Answer: The campers will be [tex]40\ miles[/tex] from their car after 12 hours.Step-by-step explanation: The missing graph is attached. The equation of the line in Slope-Intercept form is: [tex]y=mx+b[/tex] Where "m" is the slope and "b" the y-intercept. We can pick two points on the line graphed and substitute the coordinates into this formula to find the slope: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] Choosing the points (0,4) and (2,10), we get: [tex]m=\frac{4-10}{0-2}=3[/tex] We can susbstitute the point (0,4) and the slope into [tex]y=mx+b[/tex] and solve for "b": [tex]4=3(0)+b\\\\b=4[/tex] Then, the equation of this line is: [tex]y=3x+4[/tex] Since the distance in miles is represented on the y-axis and the time in hours is represented on the x-axis. we can rewrite the equation as: [tex]d=3h+4[/tex] Finally, in order to calculate the distance in miles that the campers will be from their car after 12 hours, we need to subsitute [tex]h=12[/tex] into the equation and evaluate. Then we get: [tex]d=3(12)+4\\\\d=40[/tex]