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 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:

$m=\frac{y_2-y_1}{x_2-x_1}$

The slope between the first two points is given by:

$m=\frac{9-5}{-5--7}=\frac{9-5}{-5+7}=\frac{4}{2}=2$

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

$m=\frac{13-9}{-3--5}=\frac{13-9}{-3+5}=\frac{4}{2}=2$

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

$m=\frac{17-13}{-1--3}=\frac{17-13}{-1+3}=\frac{4}{2}=2$

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)

Answer 2

Answer:

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