The other tables are partially hidden, so I cannot answer those.
I'll focus on the table in the top left corner.
The x values are: -2, 0, 2, 4
We increase by 2 each time.
The y values are: -1, 0, 1, 2
We increase by 1 each time.
Since we have a constant increase for each x and y, it means this table is linear
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Here's another way to prove that table is linear
Label the points A,B,C,D
- A = (-2,-1)
- B = (0,0)
- C = (2,1)
- D = (4,2)
Then pick the first two points to compute the slope formula.
The slope formula is:
we subtract the y values and subtract the x values in the same order, then divide those differences.
I'll skip steps but you should find the slope of line AB is 1/2.
You should also find the slope of BC is 1/2, and the slope of CD is 1/2. The fact we get the same slope each time proves that all four points are on the same line. Hence, we consider them collinear and this function is linear
Side note: The equation of this line is y = (1/2)x or y = 0.5x; whatever the x input is we cut it in half to get the y output.
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If you need a way to quickly check your work, then I recommend Desmos or GeoGebra. They are graphing calculators I use all the time. Both are free.