Question

write two equations using different operators that could be used to represent the table.

Answer 1

We must identify if we can use a linear equation

For the first table we must calculate the slopes of the lines for two pair of points

First pair of points ( 28, 7) and (12,3)

$m=\frac{y2-y1}{x2-x1}=\frac{3-7}{12-28}=\frac{-4}{-16}=\frac{1}{4}$

Second pair of points ( 4, 1) and (32,8)

$m=\frac{y2-y1}{x2-x1}=\frac{8-1}{32-4}=\frac{7}{28}=\frac{1}{4}$

We can deduce, the slopes are the same, so, they belong to the same equation wich can be Y = 1/4 * X. Other equation could be Y= X - 3/4X

For the second table we notice that the input values are the same as output values, so the equation could be Y=X. other equation could be Y= 2X - X

For the third table we notice that if we add 2 units to each input value we get the output values. So the equation could be Y= X + 2. Other equation could be Y = (2X + 4)/2