Lesson 12: Practice Problems

Problem 1

The graphs below show some data from a coffee shop menu. One of the graphs shows cost (in dollars) vs. drink volume (in ounces), and one of the graphs shows calories vs. drink volume (in ounces).

vs volume

A coordinate plane with the origin labeled “O”. The horizontal axis is labeled “volume in ounces” and the numbers 0 through 26, in increments of 2, are indicated. The vertical axis has the numbers 0 through 6 indicated. The points with coordinates 10 comma 3 point 7 5, 12 comma 4, 16 comma 4 point 5, and 24 comma 4 point 9 5 are indicated.

vs volume

A coordinate plane with the origin labeled “O”. The horizontal axis is labeled “volume in ounces” and the numbers 0 through 26, in increments of 2, are indicated. The vertical axis has the numbers 0 through 350, in increments of 50 indicated. The points 10 comma 150, 12 comma 180, 15 point 9 comma 2 hundred 38 point 5, and 24 comma 360 are indicated.

  1. Which graph is which? Give them the correct titles.

  2. Which quantities appear to be in a proportional relationship? Explain how you know.

  3. For the proportional relationship, find the constant of proportionality. What does that number mean?

Problem 2

Lin and Andre biked home from school at a steady pace. Lin biked 1.5 km and it took her 5 minutes. Andre biked 2 km and it took him 8 minutes.

  1. Draw a graph with two lines that represent the bike rides of Lin and Andre.

    blank grid

  2. For each line, highlight the point with coordinates and find .

  3. Who was biking faster?

Problem 3

Match each equation to its graph.

Graph 1

A line is graphed in the coordinate plane with the origin labeled “O”. The numbers 0 through 5 are indicated on the horizontal axis. The numbers 0 through 5, are indicated on the vertical axis. The line begins at the origin. It moves steadily upwards and to the right passing through the points with coordinates 1 comma four fifths, and 5 comma 4.

Graph 2

Graph 2 is a line graphed in the coordinate plane with the origin labeled “O”. The numbers 0 through 5 are indicated on the horizontal axis. The numbers 0 through 5 on the vertical axis. There are two evenly spaced horizontal gridlines between each integer. The line begins at the origin. It moves steadily upward and to the right passing through the points with coordinates 1 comma two-thirds, and 3 comma 2.

Graph 3

Graph 3 is a line graphed in the coordinate plane with the origin labeled “O”. The numbers 0 through 5 are indicated on the horizontal axis. The numbers 0 through 5 are indicated on the vertical axis. There are 2 evenly spaced horizontal gridlines between each integer. The line begins at the origin. It moves steadily upward and to the right passing through the points with coordinates 1 comma 1 and one-third, and 3 comma 4.

Graph 4

Graph 4 is a line graphed in the coordinate plane with the origin labeled “O”. The numbers 0 through 5 are indicated on the horizontal axis. The numbers 0 through 5 are indicated on the vertical axis. There are three evenly spaced horizonatal gridlines between each interger. The line begins at the origin. It moves gradually upwards and to the right passing through the points with coordinates 1 comma one-fourth, and 4 comma 1.

Graph 5

Graph 5 is a line graphed in the coordinate plane with the origin labeled “O”. The numbers 0 through 5 are indicated on the horizontal axis. The numbers 0 through 5 are indicated on the vertical axis. There are also horizontal gridlines midway between each integer. The line begins at the origin. It moves steeply upward and to the right, passing through the points with coordinates 1 comma 2, and 2 comma 4.

Graph 6

Graph 6 is a line graphed in the coordinate plane with the origin labeled “O”. The numbers 0 through 5 are indicated on the horizontal axis. The numbers 0 through 5 are indicated on the vertical axis. There are horizontal gridlines midway between each integer. The line begins at the origin. It moves steadily upward and to the right, passing through the points with coordinates 1 comma 1 point 5 and 2 comma 3.

  1. Graph 1

  2. Graph 2

  3. Graph 3

  4. Graph 4

  5. Graph 5

  6. Graph 6