Question

Is the relationship shown by the data linear? If so, model the data with an equation. x y 1 5 5 10 9 15 13 20 The relationship is linear; y – 5 = (x – 1). The relationship is not linear. The relationship is linear; y – 5 = (x – 1).

Answer 1

The relationship is linear; y – 5 = 5/4*(x – 1)

Explanation:

We have been given the following data set;

x: 1, 5, 9, 13

y: 5, 10, 15, 20

The values of x increase by 4 while those of y increase by 5. This would imply that the average rate of change between any pair of points is a constant and thus the relationship exhibited by the data is linear.

The average rate of change is equivalent to the slope;

(change in y) / (change in x)

Using the first two pair of points we have;

(10-5) / ( 5-1) = 5/4

The point-slope form of equation of the line is thus;

y - 5 = 5/4 (x - 1)