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

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2 Answers

     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).
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