Question

Is the relationship shown by the data linear? If so, model the data with an equation. x= -7, -5, -3 ,-1 , y = 5, 9, 13, 17

Answer 1

First we take the two points (-7,5) and (-5,9).
Compute the slope: $\frac{9-5}{-5+7}=2$
Then the linear relation may be in the following form $y=2x+b$
Since the point (-7,5) is on the line, then $5=-7(2)+b\text{ then }b=19.$
The relation is then $y=2x+19$.
We check that the other point are on the above line:
$2(-3)+19=13 \text{ OK}\\2(-1)+19=17 \text{ OK}$
We have then a linear relation.