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

Given:

The table of values is:

x :     -7          -5         -3           -1

y :      5           9         13          17

To find:

Whether the given data is linear and then find the equation.

Solution:

The given data is linear if the slope and rate of change is constant.

Slope formula:

Using the slope formula. we get

Since the rate of change is constant, i.e., 2, therefore the given data is linear.

The slope of a linear equation is 2 and it passes through the point (-7,5). So, the equation of the line is:

Adding 5 on both sides, we get

Therefore, the equation for the given data is .

fist on the left goes with the third on the right. second on the left goes with the fourth on the right. third on the left goes with the second on the right. the fourth on the left goes with first on the right