# Lesson 3

Equations for Functions

Let’s find outputs from equations.

### Problem 1

Here is an equation that represents a function: $$72x+12y=60$$.

Select all the different equations that describe the same function:

A:

$$120y + 720x = 600$$

B:

$$y = 5 - 6x$$

C:

$$2y + 12x = 10$$

D:

$$y = 5 + 6x$$

E:

$$x=\frac{5}{6} - \frac{y}{6}$$

F:

$$7x + 2y = 6$$

G:

$$x=\frac{5}{6} + \frac{y}{6}$$

### Problem 2

1. Graph a system of linear equations with no solutions.
2. Write an equation for each line you graph.
(From Unit 4, Lesson 13.)

### Problem 3

Brown rice costs $2 per pound, and beans cost$1.60 per pound. Lin has \$10 to spend on these items to make a large meal of beans and rice for a potluck dinner. Let $$b$$ be the number of pounds of beans Lin buys and $$r$$ be the number of pounds of rice she buys when she spends all her money on this meal.

1. Write an equation relating the two variables.
2. Rearrange the equation so $$b$$ is the independent variable.
3. Rearrange the equation so $$r$$ is the independent variable.

### Problem 4

Solve each equation and check your answer.

$$2x+4(3-2x)=\frac{3(2x+2)}{6}+4$$

$$4z+5=\text-3z-8$$

$$\frac12-\frac18q=\frac{q-1}{4}$$

(From Unit 4, Lesson 6.)