Answered

The cost of taking a cab is $4 plus $0.75 per mile. This can be represented using the linear function c = 0.75m + 4, where c is the cost per trip and m is the distance in miles. Graph the equation on a coordinate plane. Based on your line, what would the cost be if you were to travel 11 miles?

Verified Answer :

  • Identify the linear function representing the cab cost: \(c = 0.75m + 4\).
  • Substitute the distance \(m = 11\) into the equation to calculate the cost.
  • Perform the multiplication and addition: \(0.75 \times 11 + 4 = 8.25 + 4 = 12.25\).
  • The total cost for an 11-mile trip is \(\boxed{\$12.25}\).

Explanation

  1. Analyzing the Problem and Given Data

The problem provides a linear relationship between the cost of a cab trip and the distance traveled. The cost function is defined as \(c = 0.75m + 4\), where \(c\) is the cost in dollars and \(m\) is the distance in miles. We are tasked with finding the cost of a trip that is 11 miles long and understanding the structure of this linear function.

  1. Calculating the Cost for 11 Miles

To find the cost for a distance of 11 miles, we substitute \(m = 11\) into our given linear function:
\[c = 0.75(11) + 4\]
First, we calculate the product of 0.75 and 11:
\[0.75 \times 11 = 8.25\]
Next, we add the fixed base cost of \$4:
\[8.25 + 4 = 12.25\]
Therefore, the total cost for a 11-mile trip is \$12.25.

  1. Understanding the Graph of the Linear Function

The linear function \(c = 0.75m + 4\) represents a straight line on a coordinate plane. The y-intercept is 4, which represents the fixed base fee of the cab. The slope of the line is 0.75, representing the cost increase per mile. A graph of this function would start at the point \((0, 4)\) and rise 0.75 units for every 1 unit traveled horizontally. At \(m = 11\), the point on the line is \((11, 12.25)\).

  1. Final Answer

In conclusion, by substituting the distance into the linear function and performing the necessary arithmetic, we have determined that the cost for a 11-mile cab trip is \(\boxed{\$12.25}\).

Examples

Understanding linear functions is crucial for budgeting and managing everyday expenses. For example, if a utility company charges a fixed monthly service fee plus a rate per kilowatt-hour of electricity used, you can use a linear function to predict your monthly bill based on your energy consumption. This allows you to plan your finances effectively and make informed decisions about your energy usage. In this case, the fixed fee acts as the y-intercept, and the rate per unit acts as the slope.