The table below represents a linear function. How do I Fill in the missing entries.

Question

X= 1| 5 | 11| blank| 45

Y= -5| 1 | blank| 22 | blank|

Answer 1

Since it is a linear function you can find the slope from the first two points

m = Δy/Δx=(y₂-y₁)/(x₂-x₁)=(1-(-5))/5-1=3/2

This slope is the same for any two points from the table.

y₃-y₂=m*(x₃-x₂)

y₃ = y₂+m*(x₃-x₂) = 1+3/2*(11-5) = 10

x₄ = x₃+(y₄-y₃)/m = 11+(22-10)*2/3 = 19

y₅ = y₄+m*(x₅-x₄) = 22+3/2*(45-19) = 61

Answer 2

First,you want to find the equation for the line, you want to pick two points that don't have a blank in them, so (1,-5) and (5,1) slope is y2-y1/x2-x1, if you calculate it you will get 3/2. Now, you want to find the Y intercept, multiply 5 by 3/2, you will get 15/2, how do you go from 15/2 to 1 (2/2) you subtract 13/2, so the equation is y=3/2x-13/2.

Now you can plug in 11 which will give you 10.

For 22 you will have to plug it into y since it's a Y value so 22=3/2x-13/2 then you have to solve for x which will give you 19.

For the third blank you have to plug in 45, which will give you 61.

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