Question

One of the tables below contains (x,y) values that were generated by a linear function. Determine which table, and then write the equation of the linear function represented by the table

Please Explain

Answer 1

Table 2 & 3 do not follow any linear function, Table 1 does

Table 1
Equation:x^2+1
(1^2+1=2, 3^2+1=10, etc.)

Hope this helps:)

Answer 2

The y terms in table 1 are: 2, 10, 26, 50, 82, 122

The change in y, or the increase in y, is +8, +16, +24, +32, +40

The new sequence {8,16,24,32,40} has each term increase by 8. This second difference being constant indicates we have a quadratic function that is not linear. So table 1 is not linear.

Table 2's y values are: 2, 17, 13, 9, 5, 1

The terms start to increase but then decrease after that first increase. This inconsistency means we don't have a linear function. Table 2 is not linear.

Table 3 is linear and the function rule is: y = -4x+29

If we plug in x = 2, then we get y = -4(2)+29 = -8+29 = 21

If we plug in x = 3, we get y = -4(3)+29 = -12+29 = 17

and so on...

Each time x increases by 1, the y terms decrease by 4, therefore the slope is -4.  To find the y intercept, plug in any point from the table, say (x,y) = (2,21) and then solve for b. I'm referencing the slope intercept equation y = mx+b with m = -4 as the slope.