Question

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

The relationship is linear; y – 5 = mc019-3.jpg(x + 7).

The relationship is linear; y + 7 = mc019-1.jpg(x – 5).

The relationship is not linear.

The relationship is linear; y – 5 = mc019-2.jpg(x + 7).

Answer 1

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

Answer 2

The correct answer is:

The relationship is linear, and the equation is
y-5 = 2(x+7).

Step-by-step explanation:

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


`m=(y_2-y_1)/(x_2-x_1)`

The slope between the first two points is given by:


`m=(9-5)/(-5--7)=(9-5)/(-5+7)=(4)/(2)=2`

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


`m=(13-9)/(-3--5)=(13-9)/(-3+5)=(4)/(2)=2`

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


`m=(17-13)/(-1--3)=(17-13)/(-1+3)=(4)/(2)=2`

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)