Lesson 3

Representing Proportional Relationships

Let's graph proportional relationships.

Problem 1

Here is a graph of the proportional relationship between calories and grams of fish:

graph, horizontal axis, grams of fish, scale 0 to 300, by 50's. vertical axis, number of calories, scale 0 to 600, by 100's.
  1. Write an equation that reflects this relationship using \(x\) to represent the amount of fish in grams and \(y\) to represent the number of calories.
  2. Use your equation to complete the table: 
    grams of fish number of calories

Problem 2

Students are selling raffle tickets for a school fundraiser. They collect $24 for every 10 raffle tickets they sell.

  1. Suppose \(M\) is the amount of money the students collect for selling \(R\) raffle tickets. Write an equation that reflects the relationship between \(M\) and \(R\).
  2. Label and scale the axes and graph this situation with \(M\) on the vertical axis and \(R\) on the horizontal axis. Make sure the scale is large enough to see how much they would raise if they sell 1000 tickets.
    Blank coordinate plane.

Problem 3

Describe how you can tell whether a line’s slope is greater than 1, equal to 1, or less than 1.

(From Unit 2, Lesson 10.)

Problem 4

A line is represented by the equation \(\frac{y}{x-2}=\frac{3}{11}\). What are the coordinates of some points that lie on the line? Graph the line on graph paper.

(From Unit 2, Lesson 12.)