Lesson 11 Equations for Proportional Relationships Answer Key

1. Trail-mix graph

The equation is

$$r=\frac{3}{4}b.$$

Substituting $b=4$ gives $r=3$, so the point is B. $(4,3)$.

2. Weight of boxes

The starred point is $(1,\frac12)$: one box corresponds to one-half pound. The answer is B. Each box weighs $\frac12$ pound.

3. Flour and bread

The unit rate is

$$k=\frac{18\frac34}{5}=\frac{18.75}{5}=3.75=3\frac34$$

cups of flour per loaf. Therefore:

• A is correct: $f=3\frac34b$.
• B is incorrect: 10, 15, and 20 loaves would require 37.5, 56.25, and 75 cups, not the displayed values.
• C is incorrect: it reverses the variables; solving for loaves would give $b=\frac{4}{15}f$.
• D is correct: $(2,7.5)$, $(4,15)$, and $(6,22.5)$ all satisfy $f=3.75b$.

The selections are A and D.

4. Dog-food graph

The plotted line goes through $(0,0)$ and $(5,2)$, so

$$k=\frac{2}{5}=0.4\text{ pound per day}.$$

• A is correct: a straight line through the origin represents a proportional relationship.
• B is incorrect: $(5,2)$ means 2 pounds in 5 days, not 5 pounds in 2 days.
• C is incorrect: $(0,0)$ means that after 0 days, 0 pounds have been eaten.
• D is correct: the constant of proportionality is $0.4$.

The selections are A and D.

5. Paint cans

The wall area is

$$10\text{ ft}\times12\text{ ft}=120\text{ ft}^2.$$

Each can covers $32\text{ ft}^2$, so

$$\frac{120}{32}=3.75.$$

Len cannot buy three-fourths of a can, so he must buy 4 cans.

6. Pizza equations

Both equations are correct:

$$p=\frac14s \qquad\text{and}\qquad s=4p.$$

The table shows one pizza for every four students. The first equation gives pizzas from students; multiplying both sides by 4 produces $4p=s$, which is the second equation and gives students from pizzas. They express the same relationship with different dependent variables.