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

Answer: Scenario 1: The slope of the line in this scenario would be negative. This is because the relationship between the amount of gas used and the hours ridden is a linear relationship where the more hours Stella rides, the more gas she will use. Since each hour of riding uses 0.1 gallons of gas, the rate of change (i.e., the slope) will be negative, meaning that as the number of hours ridden increases, the amount of gas remaining in the tank will decrease.

Scenario 2: The slope of the line in this scenario would be zero. This is because there is no relationship between the number of pieces of gum in the backpack on Monday and the number of pieces of gum left on Friday. The number of pieces of gum remained the same throughout the week, so there is no change in the number of pieces of gum, and hence the slope of the line would be zero.

Explanation: