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

Answer 1

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:

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

Using the slope formula. we get

`(9-5)/(-5-(-7))=2`

`(13-9)/(-3-(-5))=2`

`(17-13)/(-1-(-3))=2`

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:

`y-y_1=m(x-x_1)`

`y-5=2(x-(-7))`

`y-5=2(x+7)`

`y-5=2x+14`

Adding 5 on both sides, we get

`y-5+5=2x+14+5`

`y=2x+19`

Therefore, the equation for the given data is
`y=2x+19`.