Explain whether the function represents by this table of values is a linear function justify your answer

Question

X g(x)
-3 3
-1 -13
1 -29
3 -45

Answer 1

A linear function is a function that can be represented by a straight line when graphed on a coordinate plane.

Looking at the table of values, we can determine if the function is linear by calculating the slope between the pairs of points. If the slope is constant between all pairs of points, then the function is linear.

Using the points (-3, 3) and (-1, -13):
slope = (change in y) / (change in x) = (-13 - 3) / (-1 - (-3)) = -16 / 2 = -8

Using the points (-1, -13) and (1, -29):
slope = (change in y) / (change in x) = (-29 - (-13)) / (1 - (-1)) = -16 / 2 = -8

Using the points (1, -29) and (3, -45):
slope = (change in y) / (change in x) = (-45 - (-29)) / (3 - 1) = -16 / 2 = -8

Since the slope between all pairs of points is constant (-8), the function represented by this table of values is a linear function.