Question

Which table represents a linear function?

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Answer 1

I can’t see the images you attached. Please either paste the four tables here or upload the image again.

Meanwhile, here’s a quick way you can tell which table shows a linear function:

1. If the x-values are equally spaced: check the differences in the y-values. If the y-differences are all the same (constant), the table is linear.
- Example: x: 1,2,3; y: 4,7,10 → y-differences: 3,3 → linear (slope m = 3).

2. If the x-values are not equally spaced: compute the slope between successive points: (y2 − y1) / (x2 − x1). If that slope is the same for every pair of points, the table is linear.
- Once you have slope m, find intercept b by b = y1 − m·x1 and verify all points satisfy y = m·x + b.

3. Edge cases:
- If two points have the same x but different y, it is not a function at all.
- If all y-values are the same, that’s linear (slope m = 0).

If you paste one of the tables here, I’ll check and tell you which one(s) are linear.