Question

find the rate of change.

time(hours)	distance (miles)
6	378
8	504
10	630

(1 point)

• \\(\frac{1}{63}\\); the car travels 1 mile every 63 hours.
• 10; the car travels 1 mile every 63 hours
• \\(\frac{63}{1}\\); the car travels 63 miles every 1 hour.
• 252; the car travels 252 miles.

Explanation:

Step1: Recall rate of change formula

The rate of change (slope) for a linear relationship between time (\(x\)) and distance (\(y\)) is given by \(\frac{\Delta y}{\Delta x}=\frac{y_2 - y_1}{x_2 - x_1}\).

Step2: Choose two points

Let's take the first two points: \((x_1,y_1)=(4,252)\) and \((x_2,y_2)=(6,378)\).

Step3: Calculate the rate of change

Substitute into the formula: \(\frac{y_2 - y_1}{x_2 - x_1}=\frac{378 - 252}{6 - 4}=\frac{126}{2}=63\). This means the distance changes by 63 miles for each 1 - hour change in time, so the rate of change is \(\frac{63}{1}\), representing the car travels 63 miles every 1 hour.

Answer:

\(\frac{63}{1}\); The car travels 63 miles every 1 hour.