Relationship B has a lesser rate than Relationship A. The graph represents Relationship A.Which table could represent Relationship B? First-quadrant graph showing a ray from the origin through the points (2, 3) and (4, 6). Horizontal axis label is Time in weeks. Vertical axis label is Plant growth in inches. A.Time (weeks) 3 6 8 10Plant growth (in.) 2.25 4.5 6 7.5 B.Time (weeks) 3 6 8 10Plant growth (in.) 4.8 9.6 12.8 16 C.Time (weeks) 3 4 6 9Plant growth (in.) 5.4 7.2 10.8 16.2 D.Time (weeks) 3 4 6 9Plant growth (in.) 6.3 8.4 12.6 18.9

Given that Relationship B has a lesser rate than Relationship A and that the graph representing Relationship A is a first-quadrant graph showing a ray from the origin through the points (2, 3) and (4, 6) where the horizontal axis label is Time in weeks and the vertical axis label is Plant growth in inches.

The rate of relationship A is given by the slope of the graph as follows:

[tex]slope= \frac{6-3}{4-2} = \frac{3}{2} =1.5[/tex]

To obtain which table could represent Relationship B, we check the slopes of the tables and see which has a lesser slope.

For table A.
Time (weeks) 3 6 8 10
Plant growth (in.) 2.25 4.5 6 7.5

[tex]slope= \frac{4.5-2.25}{6-3} = \frac{2.25}{3} =0.75[/tex]

For table B.
Time (weeks) 3 6 8 10
Plant growth (in.) 4.8 9.6 12.8 16

[tex]slope= \frac{9.6-4.8}{6-3} = \frac{4.8}{3} =1.6[/tex]

For tabe C.
Time (weeks) 3 4 6 9
Plant growth (in.) 5.4 7.2 10.8 16.2

[tex]slope= \frac{7.2-5.4}{4-3} = \frac{1.8}{1} =1.8[/tex]

For table D.
Time (weeks) 3 4 6 9
Plant growth (in.) 6.3 8.4 12.6 18.9

[tex]slope= \frac{8.4-6.3}{4-3} = \frac{2.1}{1} =2.1[/tex]

Therefore, the table that could represent Relationship B is table A.