Lesson 10

Equations and Relationships

  • Let’s match graphs and equations.

10.1: Which One Doesn't Belong: Slopes and Intercepts

Which one doesn't belong?

ACoordinate plane, x, negative 12 to 12 by 3, y, negative 12 to 12 by 3. Line drawn through 0 comma 3 and 1 point 5 comma 10 point 5.
BCoordinate plane, x, negative 12 to 12 by 3, y, negative 12 to 12 by 3. Horizontal line drawn at y = 3.

C. \(y=\text -2.5x - 7.5\)

DCoordinate plane, x, negative 16 to 16 by 4, y, negative 16 to 16 by 4. LIne drawn through 0 comma 8 and 16 comma 0.

 

10.2: What’s the Same? What’s Different?

Here are the graphs of four linear equations.

Graph A

Coordinate plane, x, negative 10 to 8 by 2, y, negative 10 to 8 by 2. Line through negative 2 0 and 0 comma 6.

Graph B

Coordinate plane, x, negative 10 to 8 by 2, y, negative 10 to 8 by 2. Line through negative 1 comma negative 4 and 1 comma 2.

Graph C

Coordinate plane, x, negative 10 to 8 by 2, y, negative 10 to 8 by 2. Line through negative 2 comma negative 2 and 2 comma 0.

Graph D

Coordinate plane, x, negative 10 to 8 by 2, y, negative 10 to 8 by 2. Line through negative 4 comma negative 1 and 0 comma 1.
  1. Which graphs have a slope of 3?
  2. Which graphs have a slope of \(\frac12\)?
  3. Which graphs have a \(y\)-intercept of -1?
  4. Which graphs have an \(x\)-intercept of -2?
  5. Graph A represents the equation \(2y - 6x = 12\). Which other equations could graph A represent?
    1. \(y - 3x = 6\)
    2. \(y = 3x + 6\)
    3. \(y = -3x + 6\)
    4. \(2y = -6x + 12\)
    5. \(4y - 12x = 12\)
    6. \(4y - 12x = 24\)
  6. Write three equations that graph B could represent.

10.3: Situations and Graphs

For each situation, find the slope and intercepts of the graph. Then, describe the meaning of the slope and intercepts. Determine if the values you come up with are reasonable answers for the situation.

  1. The printing company keeps an inventory of the number of cases of paper it has in stock.
    Coordinate plane, horizontal, number of orders, 0 to 10 by 2, vertical, cases of paper stock, 0 to 70 by 10. Line drawn from 0 comma 60 to 10 comma 20.

  2. The market value of a house is determined by the size of the house.

    Coordinate plane, horizontal, area in square feet, 0 to 300 by 50, vertical, market value in thousands of dollars, 0 to 70 by 5. Line drawn from 0 comma 10 through 250 comma 62 point 5.

  3. Tyler teaches painting classes in which the amount of money he makes depends on the number of participants he has.

    Coordinate plane, horizontal, number of participants, 0 to 7 by 1, vertical, income in dollars, 0 to 300 by 20. Line drawn from 0 comma 50 through 2 comma 120.

  4. Mai tracks the amount of money in her no-interest savings account.

    Coordinate plane, horizontal, weeks since Mai opened the account, 0 to 3 by 1, vertical, value of Mai’s account, 0 to 1,600 by 200. Line through 1 comma 600 and 2 point 5 1,300.

  5. Priya earns coins for each new level she reaches on her game. 

    Coordinate plane, horizontal, level, 0 to 4 by 1, vertical, amount of coins, 0 to 9,600 by 800. Line drawn through 0 comma 400 and 1 comma 2,400.

Summary