Graph Interpretation

Part 1

The base fee is five dollars. The base fee can be determined by finding the cost in dollars when the distance in Miles is zero. Looking at the graph, when the distance travelled in Miles is zero, the cost in dollars is five dollars. The five dollars is the initial fee before a journey is initiated. Therefore, this means that the base fee charged by the rideshare service is five dollars.

Part 2

When the distance travelled is 20 Miles, the charged fee is 50 dollars. Therefore, the rate of change can be calculated by dividing the change in cost by the distance travelled.

Therefore, the increase in cost per mile is dollars per mile.

The figure shows the final cost against the initial fee. Twenty, the denominator remains the same since the initial distance is zero, and there would thus be no need to subtract the initial distance from the final distance.

Part 3

The slope and y-intercept of the graph will be determined as follows:

Therefore, the slope is 9/4 or 2.25.

The y-intercept would be:

or 5

The intercept has been determined as such because it is the point where the graph touches the y-axis. When x = 0, y = 5. Therefore, the y-intercept becomes or 5.

Part 4

The slope-intercept equation is derived based on the following formula:

Where  and

The slope and y-intercept had already been determined before.

Therefore, the equation will be:

Part 5

The equation derived above could be used to extrapolate a 40-mile ride.

The x in the equation would be the distance travelled.

Therefore, the x would be substituted with 40.

The cost of a 40-mile ride would thus be 90 dollars.

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Assessment Instructions
Show and explain all steps in your responses to the following parts of the assignment. All mathematical steps must be formatted using the equation editor.

Graph Interpretation

Part 1: Calculate the base fee (in dollars) charged by the ride-share service.

Part 2: Calculate the rate of increase in cost in dollars per mile. Use the points (0, 5) and (20, 50) for your calculation.

Part 3: Identify the slope and y-intercept of the equation in the graph.

Part 4: Write the slope-intercept equation of the line in the graph.

Part 5: Use your equation from part 4 to extrapolate the cost of a 40-mile ride.
Please make sure you explain in words how you solved each question.