The cost of taking a cab is $4 plus $0.75 per mile. This can be represented using the linear function c=0.75m+4𝑐=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 find the cost \( c \) of taking a cab for 4.5 miles, we can substitute \( m = 4.5 \) into the linear function \( c = 0.75m + 4 \).

\[ c = 0.75(4.5) + 4 \]

Now let's calculate \( 0.75 \times 4.5 \):

\[ 0.75 \times 4.5 = 3.375 \]

Next, add 4 to this value:

\[ c = 3.375 + 4 = 7.375 \]

Now, rounding \( 7.375 \) to the nearest hundredth gives us:

\[ c \approx 7.38 \]

Thus, the corresponding dependent variable (cost) for traveling 4.5 miles is approximately $7.38.

Also, to graph the equation \( c = 0.75m + 4 \):

1. When \( m = 0 \), \( c = 4 \) (the y-intercept).
2. When \( m = 1 \), \( c = 0.75(1) + 4 = 4.75 \).
3. When \( m = 2 \), \( c = 0.75(2) + 4 = 5.50 \).
4. When \( m = 3 \), \( c = 0.75(3) + 4 = 6.25 \).
5. When \( m = 4 \), \( c = 0.75(4) + 4 = 7.00 \).
6. When \( m = 5 \), \( c = 0.75(5) + 4 = 7.75 \).
7. When \( m = 6 \), \( c = 0.75(6) + 4 = 8.50 \).

You can plot these points on a coordinate plane with \( m \) on the x-axis and \( c \) on the y-axis. The line will rise as the distance \( m \) increases, indicating that the total cost \( c \) increases with more miles traveled.