Lesson 3

Equations for Functions

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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:

\(x=\frac{5}{6} + \frac{y}{6}\)

Solution

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Problem 2

  1. Graph a system of linear equations with no solutions.
  2. Write an equation for each line you graph.
Blank coordinate plane, horizontal axis negative 8 to 8 by ones, vertical axis negative 6 to 6 by ones.

Solution

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(From Unit 5, Lesson 14.)

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.

Solution

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Problem 4

Solve each equation and check your answer.

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

\(4z+5=\text-3z-8\)

\(\frac12-\frac18q=\frac{q-1}{4}\)

Solution

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(From Unit 4, Lesson 14.)