Question

Please help me with this math problem.

Answer 1

The relationship is linear, and of the form:

`y-5=(5)/(4) (x-1)` (last option in the list of possible answers)

Explanation:

Yes, the relationship is linear. Such can be clear by examining if 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 "5":

10-5 = 5

15-10 = 5

20-15 = 5

and the respective differences between consecutive x-values of the table, always render "4":

5-1 = 4

9-5 = 4

13-9 = 4

This tells us that the associated rates of change are constant and equal to "5/4".

`(y_2-y_1)/(x_2-x_1) =(y_3-y_2)/(x_3-x_2)=(y_4-y_3)/(x_4-x_3)=(5)/(4)`

This is then the slope of the line that joints all of those points.

Now, in order to find a point-slope form for this line one can use the first pair (1, 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 = 5/4, and that we can use the point (1, 5) as the particular point to define it:

`y-y_0=m\,(x-x_0)\\y-5=(5)/(4) (x-1)`, which is in fact the last option given in the choice of answers.