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 corresponding dependent variable be if you were to travel 4.5 miles? Round your answer to the nearest hundredth.

Answer 1

To graph the equation \( c = 0.75m + 4 \), we can start by identifying a few points based on the equation. Let's calculate the cost \( c \) for some values of \( m \) (the distance in miles):

1. When \( m = 0 \): \[ c = 0.75(0) + 4 = 4 \] (Point: \( (0, 4) \))

2. When \( m = 1 \): \[ c = 0.75(1) + 4 = 0.75 + 4 = 4.75 \] (Point: \( (1, 4.75) \))

3. When \( m = 2 \): \[ c = 0.75(2) + 4 = 1.5 + 4 = 5.5 \] (Point: \( (2, 5.5) \))

4. When \( m = 3 \): \[ c = 0.75(3) + 4 = 2.25 + 4 = 6.25 \] (Point: \( (3, 6.25) \))

5. When \( m = 4 \): \[ c = 0.75(4) + 4 = 3 + 4 = 7 \] (Point: \( (4, 7) \))

6. When \( m = 4.5 \): \[ c = 0.75(4.5) + 4 = 3.375 + 4 = 7.375 \] (Point: \( (4.5, 7.375) \))

Now that we have these points, we can create a graph of the equation on a coordinate plane with \( m \) on the x-axis and \( c \) on the y-axis.

To answer the second part of your question, when you travel \( 4.5 \) miles, the corresponding dependent variable \( c \) would be \( 7.375 \).

Rounding to the nearest hundredth gives:

\[ \boxed{7.38} \]