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Question 6 of 10

The cost, c(x), for a taxi ride is given by c(x) = 3x + 2.00, where x is the
number of minutes.
On a piece of paper, graph c(x) = 3x + 2.00. Then determine which answer
matches the graph you drew, including the correct axis labels.

1 answer

To graph the cost function \( c(x) = 3x + 2 \), you'll follow these steps:

  1. Identify the function parameters:

    • This is a linear function where:
      • The slope (m) = 3
      • The y-intercept (b) = 2

  2. Plot the y-intercept:

    • Start at the point (0, 2) on the graph, which is where the taxi ride starts, even if no time has passed.

  3. Use the slope to plot additional points:

    • From the intercept (0, 2), you can use the slope to find another point.
    • Since the slope is 3, you can go up 3 units in the y-direction and 1 unit in the x-direction. This gives you the point (1, 5).

  4. Additional points from the slope:

    • From (1, 5), if you move another minute (x = 2), you’ll go up 3 more units to (2, 8).
    • You can continue this for additional values such as (3, 11) and (4, 14).

  5. Draw the line:

    • Connect the points you’ve plotted with a straight line. This will be your graph of the function \( c(x) = 3x + 2 \).

  6. Label your axes:

    • The x-axis should be labeled as "Time (minutes)".
    • The y-axis should be labeled as "Cost ($)" for the cost incurred based on the ride duration.

  7. Determine the characteristics of the graph:

    • The line will rise steeply because of the slope of 3, indicating that the cost increases significantly with each additional minute.

If you had multiple choice answers, look for a graph that features:

  • A straight line starting at (0, 2),
  • It increases steeply reflecting a slope of 3,
  • Correct axis labels for time and cost.

You now have everything you need to find the correct graph among provided options!