Relationship B has a lesser rate than Relationship A. The graph represents Relationship A.

2 answers:

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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:

$slope= \frac{6-3}{4-2} = \frac{3}{2} =1.5$

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

$slope= \frac{4.5-2.25}{6-3} = \frac{2.25}{3} =0.75$

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

 $slope= \frac{9.6-4.8}{6-3} = \frac{4.8}{3} =1.6$

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

 $slope= \frac{7.2-5.4}{4-3} = \frac{1.8}{1} =1.8$

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

 $slope= \frac{8.4-6.3}{4-3} = \frac{2.1}{1} =2.1$ 

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