Question

Two scenarios are written below. Describe if the slope of the line of each relationship would be positive, negative, zero, or undefined and tell how you know.

Scenario 1
Stella rides dirt bikes. On Friday, Stella fills up the gas tank with 2 gallons of gas and rides all weekend. Each hour of riding using 0.1 gallons of gas.

Scenario 2
Scout has three pieces of gum in a backpack on Monday. On Friday, Scout finds that there are three pieces of gum left.

Answer 1

Scenario 1: The slope of the line would be negative because as time increases (i.e., more hours of riding), the amount of gas in the tank decreases. The rate of change would be -0.1 gallons of gas per hour of riding.

Scenario 2: The slope of the line would be zero because there is no change in the number of gum pieces over time. The rate of change would be 0 pieces of gum per day.

Answer 2

Scenario 1:
The slope of the line of this relationship would be negative because as time (or hours of riding) increases, the amount of gas in the tank decreases. The rate of change is constant at 0.1 gallons of gas per hour of riding, so the slope would be a straight line with a negative slope.

Scenario 2:
The slope of the line of this relationship would be zero because there is no change in the number of pieces of gum over time. The line representing this relationship would be a horizontal line with a slope of zero.