Question

Bridget has 13 gallons of gasoline to use for her lawn-mowing business. She uses gasoline in the lawn mower at a constant rate. Let x represent the number of lawns mowed and y represent the amount of gasoline remaining. Look at the graph of this function. Construct the function for this scenario. A first quadrant graph is shown. The horizontal axis is labeled Lawns. The vertical axis is labeled Gas in gallons. A line passes decreases through the points, zero comma thirteen, twenty comma eight, and fifty-two comma zero. Drag the numbers or intervals into the boxes to correctly complete the sentences

Answer 1

Bridget's gas usage forms a linear function defined by y = (-8/5)x + 13. This means each lawn mowed reduces gas by 8/5 gallons, starting with 13 gallons initially.

Gathering Information:

Bridget has 13 gallons initially (y-intercept).

Each lawn mowed reduces the remaining gasoline by a constant amount (slope).

We need to find the equation of the line representing this relationship (y = mx + b).

Determining the Slope (m):

a) Choose two convenient points from the graph:

Point 1: (0, 13) (initial point)

Point 2: (5, 5) (after 5 lawns mowed)

b) Calculate the slope (m) using the formula:

m = (y2 - y1) / (x2 - x1)

m = (5 - 13) / (5 - 0)

m = -8 / 5

Finding the y-intercept (b):

We already know the y-intercept is 13 because it's the initial amount of gasoline (when x = 0).

Constructing the Equation:

Now that we have the slope (m = -8/5) and the y-intercept (b = 13), the equation becomes:

y = (-8/5)x + 13

Verification:

This equation accurately reflects the linear relationship between x (lawns mowed) and y (remaining gasoline):

When x = 0 (no lawns mowed), y = 13 (13 gallons left).

When x = 5 (5 lawns mowed), y = 5 (5 gallons left).

Therefore, the equation y = (-8/5)x + 13 is the solution that represents Bridget's gas usage.