Answer: The correct option is (D) [tex]p=2a+3.[/tex]
Step-by-step explanation: Given that a farmer picked 3 more peaches than 2 times the apples. The following table shows how the number of peaches, p, depends on the number of apples, a.
a 2 3 4 5
p 7 9 11 13
We are to choose the correct equation that represents the rule.
Since the relation between the number of apples and peaches is a linear one, so the resulting equation will be a linear equation in p and a.
And, the graph will be a straight line.
From the above table, we can see that the line passes through the points
(a, p) = (2, 7) and (3, 9).
So, the slope of the line will be
[tex]m=\dfrac{9-7}{3-2}=2.[/tex]
Since the line passes through (2, 7), so its equation will be
[tex]p-7=m(a-2)\\\\\Rightarrow p-7=2(a-2)\\\\\Rightarrow p-7=2a-4\\\\\Rightarrow p=2a+3.[/tex]
Thus, teh required equation is [tex]p=2a+3.[/tex]
Option (D) is CORRECT.
