Relationship B has a greater rate than Relationship A. The graph represents Relationship A.
Which table could represent Relationship B?
A.
Time (weeks) -2- -5- -6- -9-
Plant growth (in.) -1.2- -3 -3.6- -5.4-
B.
Time (weeks) -2- -5- -6- -9-
Plant growth (in.) -1.4- -3.5- -4.2- -6.3-
C.
Time (weeks) -2- -5- -6- -9-
Plant growth (in.) -1.6- -4- -4.8- -7.2-
D.
Time (weeks) -3- -4- -6- -9-
Plant growth (in.) -1.5- -2- -3- -4.5-
Answer (3)
The table that could represent Relationship B to have a greater rate than Relationship A is;
Table C
To find the rates of the various tables, we will use the formula;
Rate = Δy/Δx
Using the coordinates on the graph (4, 3) and (8, 6), we have;
Rate = (6 - 3)/(8 - 4)
Rate = 3/4
Rate = 0.75
For Table A;
From the graph, we can see the y-axis represents plant growth while the x-axis represents time.
Thus, using the coordinates (2, 1.2) and (5, 3), we have;
Rate = (3 - 1.2))/(5 - 2)
Rate = 0.6
For Table B;
Using the coordinates (2, 1.4) and (5, 3.5)
Rate = (3.5 - 1.4)/(5 - 2)
Rate = 0.7
For Table C;
Using the coordinates (2, 1.6) and (5, 4) gives;
Rate = (4 - 1.6)/(5 - 2)
Rate = 0.8
For Table D;
Using the coordinates (3, 1.5) and (4, 2) we have;
Rate = (2 - 1.5)/(4 - 3)
Rate = 0.5
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The rate would be the gradient, defined by dy/dx. For graph A this would be (6-3)/(8-4)= 3/4. So any table showing a gradient of over 3/4 would have a faster rate. Table A: (3-1.2)/(5-2)= 1.8/3= 0.6, less than 0.75 Table B: (3.5-1.4)/(5-2)= 2.1/3= 0.7, still less than 0.75 Table C: (4-1.6)/(5-2)= 2.4/3= 0.8. This is a higher gradient than 0.75 in graph A. therefore table C shows a faster rate.
The table that represents Relationship B, which has a greater rate than Relationship A, is Table D with a rate of -0.5. This is greater than the rates of Tables A, B, and C, which are all more negative. Therefore, the chosen answer is Table D.
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