What is the rule for the function shown in the table?

Question

x -1, 0, 1, 2
y -2, 1, 4, 7

a. y=1/3x+1
b. y=3x+1
c. y=1/3x
d. y=1/2+1******

Please help

Answer 1

looks like (b) to me.

1/2 x would leave extra 1/2's at all the odd values of x.

Answer 2

x1 = - 1

x2 = 0

x3 = 1

x4 = 2

x2 - x1 = 0 - ( - 1 ) = 0 + 1 = 1

x3 - x2 = 1 - 0 = 1

x4 - x3 = 2 - 1 = 1

y1 = - 2

y2 = 1

y3 = 4

y4 = 7

y2 - y1 = 1 - ( - 2 ) = 1 + 2 = 3

y3 - y2 = 4 - 1 = 3

y4 - y3 = 7 - 4 = 3

Since both x and y increase by a constant difference ( x increases by 1, and y increases by 3 ), this is a linear function.

You can think of it as if given two points. Let's take the first two:

( - 1 , - 2 ) and ( 0 , 1 )

Find ind the slope:

m = ( y2 - y1 ) / ( x2 - x1 )

m = [ 1 - ( - 2 ) ] / [ 0 - ( - 1 ) ]

m = ( 1 + 2 ) / ( 0 + 1 )

m = 3 / 1

m = 3

Using point slope form with the first point ( - 1 , - 2 )

y – y1 = m ( x – x1 )

y - ( - 2 ) = 3 [ x - ( - 1 ) ]

y + 2 = 3 ( x + 1 )

y + 2 = 3 x + 3 Subtract 2 to both sides

y + 2 - 2 = 3 x + 3 - 2

y = 3 x + 1

Proof :

x = - 1

y = 3 x + 1 = 3 * ( - 1 ) + 1 = - 3 + 1 = - 2

x = 0

y = 3 x + 1 = 3 * 0 + 1 = 0 + 1 = 1

x = 1

y = 3 x + 1 = 3 * 1 + 1 = 3 + 1 = 4

x = 2

y = 3 x + 1 = 3 * 2 + 1 = 6 + 1 = 7

Answer b

Answer 3

THank you soooo much! I see now

Answer 4

They are correct!
y= 3x + 1 is right