Question

Aimee noticed her plant grew Two-thirds of an inch every week since it sprouted. She created this graph to show its growth.

On a coordinate plane, a graph titled Plant Growth has Weeks Since Sprouting on the x-axis and Height (inches) on the y-axis. Points (3, 2) and (6, 4) are plotted.

Which statement about Aimee’s graph is true?
Aimee’s graph is correct because the ratio Two-thirds is to 1 is equal to 2:3, which her graph shows in each point.
Aimee’s graph is incorrect because the ratio Two-thirds is to 1 is equal to 3:2, so she should have switched her points.
Aimee’s graph is correct because it shows 3 inches of plant growth every two weeks.
Aimee’s graph is incorrect because it shows 2 inches of plant growth with each point instead of Two-thirds of an inch.

Answer 1

The first statement is true.

Check the slope: (4 − 2) / (6 − 3) = 2/3 inches per week, which matches "two-thirds of an inch every week." Saying "two-thirds : 1 = 2 : 3" is another way of expressing the same rate (2 inches every 3 weeks), which the points (3,2) and (6,4) show.