Question

If lines joined each given point on the graph to the origin, which points would be on lines that represent a unit rate greater than the one represented in the table?

Answer 1

The first three, (2, 8), (3, 9) and (4, 10).

Explanation:

The unit rate, or rate of change, is another term for the slope.

The formula for slope is

`m=(y_2-y_1)/(x_2-x_1)`.

The slope in the table would be given by

m = (22-11)/(10-5) = 11/5 = 2.2.

For the slope of the line that goes through (2, 8) and (0, 0), we have

m = (8-0)/(2-0) = 8/2 = 4. This is greater than 2.2.

For the slope of the line that goes through (3, 9) and (0, 0), we have

m = (9-0)/(3-0) = 9/3 = 3. This is greater than 2.2.

For the slope of the line that goes through (4, 10) and (0, 0), we have

m = (10-0)/(4-0)/ = 10/4 = 2.5. This is greater than 2.2.

For the slope of the line that goes through (5, 8) and (0, 0), we have

m = (8-0)/(5-0) = 8/5 = 1.6. This is not greater than 2.2.

For the slope of the line that goes through (6, 7) and (0, 0), we have

m = (7-0)/(6-0) = 7/6 = 1.16. this is not greater than 2.2.

For the slope of the line that goes through (7, 6) and (0, 0), we have

m = (6-0)/(7-0) = 6/7 = 0.86. This is not greater than 2.2.