Question

Could the table of (x,y) pairs have been generated by a linear function?
Table: x: -2, 1, 4, 6
y: -1, 0, 3, 5

Answer 1

Yes, the table of (x,y) pairs could have been generated by a linear function. To check, we can calculate the slope of the line passing through these points:

Slope (m) = (change in y) / (change in x) = (5 - (-1)) / (6 - (-2)) = 6 / 8 = 3/4

Now that we have the slope, we can check if the equation of the line passing through these points is of the form y = mx + b. Plugging in one of the points, for example (1,0):

0 = (3/4)(1) + b
0 = 3/4 + b
b = -3/4

So the equation of the line passing through these points is y = (3/4)x - 3/4, which is a linear function.