Question

Please help me with this math problem

Answer 1

Yes, the relationship is linear and given by:

`y-5=2\,(x+7)`; which is the second option given among the list of answers

Explanation:

This problem is similar to the previous one you asked. We are going to proceed in a similar way.

Yes, the relationship is linear. Again, examine the rate of change when using different pairs of (x ,)y coordinates. Notice for example that when you do the difference between consecutive y-values of the table, you always get "4":

9-5 = 4

13-9 = 4

17-13 = 4

and the associated differences between consecutive x-values of the table, always render "2":

-5-(-7) = 2

-3-(-5) = 2

-1-(-3) = 2

This tells us that the associated rates of change are always the same and equal to "4/2 = 2".

So, this is the slope of the line that connects all of those points.

Now, in order to find a point-slope form for this line one can use the first pair (-7, 5) for the point we want the line to go through, and apply the general slope-point for a line knowing that the slope m = 2, and that we will be using the point (-7, 5) to define it:

`y-y_0=m\,(x-x_0)\\y-5=2\,(x-(-7))\\y-5=2\,(x+7)`

which is in fact the second option given in the list of answers.