An architect needs to determine the slope between two points on a ski lift. The two points have been identified as (25, 30) and (125, 50), where x is the horizontal distance and y is the vertical distance from the bottom of the lift. Assuming the lift runs in a straight line, what is the slope of the line between the two points?

(Write your answer in simplest form, using / for a fraction bar if needed.)

Question

An architect needs to determine the slope between two points on a ski lift. The two points have been identified as (25, 30) and (125, 50), where x is the horizontal distance and y is the vertical distance from the bottom of the lift. Assuming the lift runs in a straight line, what is the slope of the line between the two points? 

(Write your answer in simplest form, using / for a fraction bar if needed.)

hero · Answer

Using y = mx + b, substitute the points to form two equations: 

30 = 25m + b
50 = 125m + b

Isolate b in each equation:

b = 30 - 25m
b = 50 - 125m

Set b = b, then solve for m:
30 - 25m = 50 - 125m
125m - 25m = 50 - 30
100m = 20
     m = 20/100
     m = 1/5

hero · Answer

Remember, m means slope in y = mx + b, therefore the slope is 1/5