Write a rule for the linear in the table

The answer is C. If you plug in the x into the equation, you will get your y.

The only things you need are two points.
I'm going to pick (1,-7) and (2,-10)

Watch the magic happen...

Given (1,-7) and (2,-10) as points the line passes through, you can first find the slope of the line:
(y2-y1)/(x2-x1) where (x1,y1) and (x2,y2) are the points.
[-10-(-7)]/(2-1) (plug in the numbers)
-3/1
-3
The slope is -3

Now plug the information into point-slope form.
Slope: -3
1 point: (1,-7)
Point slope form: y-y1=m(x-x1)
y-(-7)=-3(x-1) (plug in the numbers)
y+7=-3(x-1) (simplify)

Now change it into slope-intercept form.
y+7=-3x+3 (distribute)
y=-3x-4 (subtract 7 from both sides to isolate y)


C) f(x)=-3x-4

I apologize for switching out function notation, but I did it to make things easier.

Also, now you know how to do this without having to plug every point in to each equation they give you. Now you don't NEED them to even give you equations for choices.

Best of luck!