Question

Select all that apply. In a linear function: Δy = 0 Δx = 0 Δy = n Δx = n Δy = -n Δx = -n

Answer 1

Answers: All the options are right and have a special meaning.

Explanation:

1) Δy = 0

Means y is constant, which is also that the slope is zero.

The function is a horizontal line (paralell to the x-axis)

2) Δx = 0

Means x is constant, the slope is not defined (∞).

The function is a vertical line (parallel to the y-axis)

3) Δy = n

Means that the change in y is constant. So, only if the change in x is also constant the slope is constant and the function is linear.

This is because the slope is Δy / Δx.

4) Δx = n

Means the change in x is constant. So, only if Δy is constant it is a linear function, for the same reason explained above

5) Δy = -n and and 6) Δx = -n

Same reasoning of 3 and 4.