Question

the table shows the distance traveled over time while traveling at a constant speed.
distance vs. time
time in minutes (x) | distance in meters (y)
1 | 1,200
2 | 2,400
3 | 3,600
4 | 4,800
what is the rate of change in the y-values with respect to the x-values?
○ \\(\frac{1}{900}\\) minutes per meter
○ \\(\frac{1}{1,200}\\) minutes per meter
○ 900 meters per minute
○ 1,200 meters per minute

Explanation:

Step1: Recall rate of change formula

The rate of change (slope) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(\frac{y_2 - y_1}{x_2 - x_1}\). Here, \(x\) is time (minutes) and \(y\) is distance (meters). We can take two points, e.g., \((1, 1200)\) and \((2, 2400)\).

Step2: Calculate the rate of change

Using the formula, \(\frac{2400 - 1200}{2 - 1}=\frac{1200}{1}=1200\) meters per minute. This represents the change in \(y\) (distance) with respect to \(x\) (time), so it's 1200 meters per minute.

Answer:

D. 1,200 meters per minute (assuming the options are labeled A - D as per typical multiple - choice, with the last option being 1,200 meters per minute)