Question

1.3 proportional graphs
for 1 and 2, use the graph shown to the right.

1. find the constant of proportionality.

k =

1. use a sentence to explain what the constant of proportionality means in this situation.

Explanation:

Step1: Recall the formula for constant of proportionality

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

Step2: Substitute the values from the point \((6,72)\)

Given the point \((x = 6,y = 72)\), then \(k=\frac{72}{6}\).

Step3: Calculate the value of \(k\)

\(\frac{72}{6}=12\)

Answer:

1. \(k = 12\)
2. In this situation, the constant of proportionality \(k = 12\) means that for every 1 unit increase in the independent variable (let's assume it's time in hours, for example), the distance (in miles) increases by 12. So, the rate of change of distance with respect to the other variable is 12 miles per unit (of the other variable).