Question

Work with a partner. Have one person create a proportional relationship in an equation format, table, and a graph. Have the other person find the unit rate or slope for each format. Then reverse the roles.

Answer 1

First partner creates the proportional relationship:

Equation: y = 2x

Table:

| x | y |
|----|----|
| 1 | 2 |
| 2 | 4 |
| 3 | 6 |
| 4 | 8 |
| 5 | 10 |

Graph:

(See graph where x and y are plotted on a coordinate plane with a straight line passing through all the points.)

Second partner finds the unit rate or slope for each format:

For equation: The unit rate is 2, as the coefficient of x is 2.

For table: The unit rate can be found by dividing the change in y by the change in x. For example, for x=1 to x=2, y changes from 2 to 4, so the unit rate is (4-2)/(2-1) = 2.

For graph: The slope of the line representing the proportional relationship is also 2.

Roles are reversed:

Second partner creates the proportional relationship:

Equation: y = 3x

Table:

| x | y |
|----|----|
| 1 | 3 |
| 2 | 6 |
| 3 | 9 |
| 4 | 12 |
| 5 | 15 |

Graph:

(See graph where x and y are plotted on a coordinate plane with a straight line passing through all the points.)

First partner finds the unit rate or slope for each format:

For equation: The unit rate is 3, as the coefficient of x is 3.

For table: The unit rate can be found by dividing the change in y by the change in x. For example, for x=1 to x=2, y changes from 3 to 6, so the unit rate is (6-3)/(2-1) = 3.

For graph: The slope of the line representing the proportional relationship is also 3.