Question

A climber is on a hike. After 2 hours he is at an altitude of 400 feet. After 6 hours, he is at an altitude of 700 feet.

Which equation represent the situation?

A. y−700=200(x−6)
B. y−700=300(x−6)
C. y−6=75(x−700)
D. y−700=75(x−6)

Answer 1

The correct answer is D.

The climber is climbing at a rate of 75 feet per hour. This can be found by taking the difference in altitude between 2 hours and 6 hours, which is 300 feet, and dividing by the difference in time, which is 4 hours. This gives us a rate of 75 feet per hour.

To find the equation that represents the situation, we can use the point-slope formula. The point-slope formula is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. In this case, the slope is 75 and the point is (6, 700). Substituting these values into the point-slope formula, we get y - 700 = 75(x - 6).

Therefore, the equation that represents the situation is y - 700 = 75(x - 6).