Question

The two graphs below compare the gallons of gasoline used and the total distance traveled for two different cars.

Car 1
A graph has gallons of gasoline used on the x-axis and miles traveled on the y-axis. A line goes through points (2, 50) and (4, 100).
Car 2
A graph has gallons of gasoline used on the x-axis and miles traveled on the y-axis. A line goes through points (2, 40) and (4, 80).

Which comparison of the slopes of the two lines is accurate?

Answer 1

B) The slope of Car 1’s graph is 5 greater than the slope of Car 2’s graph.

I just took the quiz on edge

Answer 2

s₁ > s₂

Is accurate comparison

Explanation:

If we have two different point for a straight line the slope of such line is given by:

P₁ = ( x₁ , y₁ ) P₂ = ( x₂ , y₂ )

The slope of the line is

s₁ = (y₂ - y₁ ) / ( x₂ - x₁)

Then for the pairs of points:

P₁ (2 , 50 ) and P₂ ( 4 , 100)

y₂ - y₁ = 100 - 50 ⇒ y₂ - y₁ = 50

and

( x₂ - x₁ ) ⇒ 4 - 2 = 2

Then

s₁ = 50/2

s₁ = 25

In the second case

Points

P₁ ( 2 , 40 ) P₂ ( 4 , 80 )

s₂ = (y₂ - y₁ ) / ( x₂ - x₁)

y₂ - y₁ = 80 - 40 = 40

x₂ - x₁ = 4 - 2 = 2

s₂ = 40/2

s₂ = 20

Then

s₁ > s₂

Is accurate comparison