Question

PLEASE HELP FAST :(

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

a) The relationship is not linear.

b) The relationship is linear; y - 5 = -1/2(x + 7)

c) The relationship is linear; y + 7 = 1/2(x - 5)

d) The relationship is linear; y – 5 = 2(x + 7).

Answer 1

Write the equation of the line passing through the points (-7,5) and (-5,9):

`y-5= (9-5)/(-5-(-7)) (x-(-7)) \\ y-5= (4)/(2)(x+7) \\ y-5=2(x+7)`.
You also have another two points (-3,13) and (-1,17). Look whether coordinates of these points satisfy the line equation:

1. For (-3,13) you have

`13-5=2(-3+7) \\ \{8=8\}`;

2. For (-1,17) you have

`17-5=2(-1+7) \\ \{12=12\}`.

Conclusion: All four points lie on the line y-5=2(x+7), so the relationship shown by the data is linear.

Answer: Correct choice is D.