Question

5.

Is the relationship shown by the data linear? If so, model the data with an equation.


x y
–7 5
–5 9
–3 13
–1 17
A. The relationship is linear; y + 7 = 1/2(x – 5).
B. The relationship is linear; y – 5 = -1/2(x + 7).
C. The relationship is linear; y – 5 = 2(x + 7).
D. The relationship is not linear.

Answer 1

C. The relationship is linear; y – 5 = 2(x + 7).

Explanation:

The correct answer is:

The relationship is linear, and the equation is

y-5 = 2(x+7).

Explanation:

To determine if the relationship is linear, we find the slope between each pair of points. Slope is given by the formula:

The slope between the first two points is given by:

The slope between the second pair of points is given by:

The slope between the third pair of points is given by:

Since the slope is the same throughout the data, the relationship is linear and the slope is 2.

To write the equation, we use point-slope form, which is:

y-y₁ = m(x-x₁)

Using the first point, we have:

y-5 = 2(x--7)

y-5 = 2(x+7)

The answer is The relationship is linear; y - 5 = 2(x + 7).