Question

1. use the graph below to answer the questions on the right.

a. what is the constant of proportionality?
b. explain what the c.o.p. means in this problem.
c. what is another point that could be on this graph, select a point that is not shown.

Explanation:

Step1: Find two points on the line

We can use the points (2, 1.00) and (4, 2.00) from the graph.

Step2: Calculate the constant of proportionality (k)

The formula for the constant of proportionality in a proportional - relationship $y = kx$ is $k=\frac{y}{x}$. Using the point (2, 1.00), $k=\frac{1.00}{2}=0.5$.

Step3: Explain the C.O.P.

The constant of proportionality (C.O.P.) of 0.5 means that each taco costs $0.50$. For every taco purchased, the cost increases by $0.50$.

Step4: Find another point

If we use the equation $y = 0.5x$, when $x = 8$, $y=0.5\times8 = 4.00$. So the point (8, 4.00) could be on the graph.

Answer:

a. 0.5
b. Each taco costs $0.50. The cost increases by $0.50 for every taco purchased.
c. (8, 4.00)