Question

the graph shows a proportional relationship between a familys distance from home and the time they spent driving. what is the constant of proportionality? what does the point (1,49) represent? the constant of proportionality is miles per hour

Explanation:

Step1: Recall the formula for constant of proportionality

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

Step2: Use the point \((1,49)\) to find \(k\)

Substitute \(x = 1\) and \(y=49\) into \(k=\frac{y}{x}\). So, \(k=\frac{49}{1}\)

In the context of distance (\(y\)) and time (\(x\)) relationship (\(y = kx\)), when \(x = 1\) (1 hour of driving), \(y=49\) (distance from home is 49 miles). So the point \((1,49)\) represents that the family is 49 miles from home after 1 hour of driving.

Answer:

49

For the meaning of the point \((1,49)\):