A linear relationship is shown in the table
Time (hours) 2 4 6 8
Distance (miles) 6 12 18 24
Is the linear relationship also proportional? Explain.
a) Yes, there is no constant of proportionality.
b) No, there is no constant of proportionality.
c) Yes, the constant of proportionality is 3.
d) No, the constant of proportionality is 3.
b) No, there is no constant of proportionality.
The relationship between time and distance is linear since the data points lie on a straight line when plotted on a graph. However, for a relationship to be proportional, there must be a constant ratio between the two variables. In this case, the ratio of distance to time is not constant. For example, when time is 2 hours, distance is 6 miles (ratio of 3), but when time is 4 hours, distance is 12 miles (ratio of 3 as well). Therefore, the relationship is linear but not proportional.