Question

malik rides his scooter at a constant rate. the table shows the proportional relationship between the time in seconds and the distance traveled in feet. find the constant of proportionality that represents the number of feet malik traveled per second. this is the number that you can always multiply the time in seconds by to find the distance traveled in feet. table: time in seconds, x (0, 10, 15, 25); distance traveled in feet, y (0, 110, 165, 275) graph: distance traveled (feet) on y - axis, time (seconds) on x - axis, line passing through (0,0), (10,110), (15,165), (25,275) the constant of proportionality that represents the number of feet malik travels per second is \\(\square\\).

Explanation:

Step1: Recall the formula for constant of proportionality

For a proportional relationship \( y = kx \), the constant of proportionality \( k \) is given by \( k=\frac{y}{x} \), where \( y \) is the distance and \( x \) is the time.

Step2: Use a data point from the table

Let's take the data point \( x = 10 \) seconds and \( y = 110 \) feet. Substitute into the formula \( k=\frac{y}{x} \).
\( k=\frac{110}{10} = 11 \).
We can check with another point, say \( x = 15 \) and \( y = 165 \). \( k=\frac{165}{15}=11 \), and \( x = 25 \), \( y = 275 \) gives \( k=\frac{275}{25}=11 \). So the constant of proportionality is consistent.

Answer:

11