Question

4-50 complete the proportion table below and graph the results.

pounds of nails	2	3	5	6	8	10	20	x

a. what is the unit rate (price) of the graph?
b. what does the unit rate (price) tell you about the cost of the nails?

Explanation:

Part (a)

Step1: Identify two points

We can use the pair (5, 2.15) or (6, 2.58) or (10, 4.3) or (20, 8.60). Let's take (5, 2.15).

Step2: Calculate unit rate

Unit rate is cost per pound, so divide cost by pounds. For (5, 2.15), unit rate = $\frac{2.15}{5}$ = 0.43 dollars per pound. Let's check with another pair, (10, 4.3): $\frac{4.3}{10}$ = 0.43. Also, (20, 8.60): $\frac{8.60}{20}$ = 0.43. So the unit rate is consistent.

The unit rate represents the cost for one pound of nails. So a unit rate of $\$0.43$ per pound means that each pound of nails costs $\$0.43$. This tells us the cost per unit quantity (per pound) of the nails, so we can determine the total cost by multiplying the number of pounds by 0.43.

Answer:

The unit rate (price) of the graph is $\$0.43$ per pound of nails.

Part (b)