To graph the equation \( c = 0.75m + 4 \) and find the corresponding cost for traveling 4.5 miles, we can start by plugging in \( m = 4.5 \) into the equation.
\[ c = 0.75(4.5) + 4 \]
Calculating \( 0.75 \times 4.5 \):
\[ 0.75 \times 4.5 = 3.375 \]
Now add 4:
\[ c = 3.375 + 4 = 7.375 \]
Rounding to the nearest hundredth, the corresponding cost \( c \) for traveling 4.5 miles would be:
\[ \text{Cost} \approx 7.38 \]
Thus, the dependent variable, or the cost for traveling 4.5 miles, is $7.38.
To graph the equation, you would create a coordinate plane with the x-axis representing miles (m) and the y-axis representing cost (c). The line would start at \( c = 4 \) when \( m = 0 \) (the base fare) and increase with a slope of \( 0.75 \). You would plot points based on various distances (e.g., (0, 4), (1, 4.75), (2, 5.50), (3, 6.25), (4.5, 7.375), etc.) and connect them to form a straight line.