Which point lies on the line with point-slope equation y + 5 = 2(x + 8)?

Question

A. (-8, 5) B. (8, -5) C. (-8,-5) D. (8,5)

Answer 1

     y + 5 = 2(x + 8)

 

=> distribute the 2 on the right hand side of the equation into each term inside the parentheses to get:

 

     y + 5 = 2x + 16

 

=> subtract 5 from both sides of the equation to get:

 

     y = 2x + 11

 

Now that you have the equation in this form (slope-intercept form) it is easy to rule out choices B and D since the x-coordinate for each of these points is 8 and so the right hand side of the equation will be 27 which obviously does not equal 5 or -5.

 

For choice A, we have that x=-8 and y=5. So we get

 

     5 = 2(-8) + 11     ==>     5 = -16 + 11     ==>     5 ≠ -5

 

For choice C, we have that x=-8 and y=-5. From the calculation from choice A, we that -5 = -5. 

Thus, the point that lies on the line with the slope-intercept form y = 2x + 11 is choice C (-8, -5).

Answer 2

Two ways to do it

 

1)Brute force plug & chug all candidates (never fails)

2)Better way: Note that a point is the "zeros" of each side

 

ie (x+8), (y+5) -----> (x,y)=(-8,-5)

 

That is the advantage of this form