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Use the table to answer the question.

l A(l)
2 8
4 16
6 24
8 32
Kalani is trying to decide how large she wants the total area of her garden to be. The table shows some of the possibilities she is considering for the length of one side (l) and the total area of the garden, A(l) . Which of the following equations describes the relationship between side length and area, as outlined in this table, using function notation?

(1 point)
Responses

A(l)=2l
upper A left parenthesis l right parenthesis equals 2 l

A(w)=l+2
upper A left parenthesis w right parenthesis equals l plus 2

A(l)=4l
upper A left parenthesis l right parenthesis equals 4 l

A(w)=l+4

1 answer

To determine the correct equation that describes the relationship between the side length (l) and the total area (A(l)) based on the table provided:

  • When \( l = 2 \), \( A(2) = 8 \)
  • When \( l = 4 \), \( A(4) = 16 \)
  • When \( l = 6 \), \( A(6) = 24 \)
  • When \( l = 8 \), \( A(8) = 32 \)

We can observe that the total area \( A(l) \) appears to be proportional to the side length \( l \). Calculating the values of \( A(l) / l \):

  • \( A(2) / 2 = 8 / 2 = 4 \)
  • \( A(4) / 4 = 16 / 4 = 4 \)
  • \( A(6) / 6 = 24 / 6 = 4 \)
  • \( A(8) / 8 = 32 / 8 = 4 \)

In each case, the result of \( A(l) / l \) is consistently 4. This suggests a linear relationship where the area is calculated using the formula:

\[ A(l) = 4l \]

Thus, the correct equation that describes the relationship is:

\[ A(l) = 4l \]

So the correct response is:

A(l) = 4l