Question

Is the above relationship a linear function
1. Yes
2. No

Answer 1

Yes, the one above is a linear function

Answer 2

yes, it is linear.

Explanation:

If the function is linear, the rate of increase between two pairs must always be equal.

This can be calculated as:

s = (y2 - y1)/(x2 - x1)

Where if we have a linear relationship y(x); we would have:

y2 = y(x2)

y1 = y(x1)

In the graph we can see the pairs:

(0, 46)

(1, 39)

(2, 32)

(3, 25)

Then the slopes are:

for the first two points.

s = (39 - 46)/(1 - 0) = -7

for second and third:

s = (32 - 39)/(2 - 1) = -7

for third and fourth:

s = (25 - 32)/(3 - 2) = -7

So this relationship is linear, because we always have the same slope.