Question

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.(1 point)

Answer 1

To graph the equation \( c = 0.75m + 4 \), we first identify the variables:

- \( c \) is the cost of the cab trip.
- \( m \) is the distance in miles.

### Step 1: Identify key points

1. **Y-intercept**: When \( m = 0 \) (i.e., no miles traveled), the cost \( c \) is:
\[
c = 0.75(0) + 4 = 4
\]
This gives us the point \( (0, 4) \).

2. **X-intercept**: To find where the cost is zero (though practically it won't be used):
\[
0 = 0.75m + 4 \implies 0.75m = -4 \implies m = -\frac{4}{0.75} \approx -5.33
\]
This gives us a theoretical point on the negative side \( (-5.33, 0) \) but isn't practical for our scenario.

3. **Additional point**: Let's calculate the cost for another mile, say \( m = 4 \):
\[
c = 0.75(4) + 4 = 3 + 4 = 7
\]
This gives us the point \( (4, 7) \).

### Step 2: Graph the equation

You would plot the points \( (0, 4) \) and \( (4, 7) \) on a coordinate plane and draw a straight line through those points, extending it in both directions.

### Step 3: Find the cost for traveling 4.5 miles

Now plug \( m = 4.5 \) into the equation:
\[
c = 0.75(4.5) + 4 = 3.375 + 4 = 7.375
\]

### Final Answer
Rounded to the nearest hundredth, the corresponding dependent variable (cost) for traveling 4.5 miles would be:
\[
\text{Cost} = 7.38
\]