Find an equation for line ...algebra please help?

Question

Find an equation for line ...
***Multiple choice***


Through (8,1) and perpendicular to y = 4/3x + 4.
(4 over 3)

A. y = -4/3x + 35/3
B. y = -3/4x + 7
C. y = 3/4x - 5
D. y = 4/3x - 29/3


Through (5, -6) and parallel to y =-1/2x + 4.

A. y = 2x - 16
B. y = -2x + 4
C. y = -1/2x - 7/2
D. y = 1/2x -17/2


Through (-3, 6) and vertical.

A. x = 6
B. y = -3
C. y = 6
D. x = -3

Answer 1

First one is B, as you get a perpendicular line by inverting and negating the slope. That means the slope of the new line is -3/4 and there is only one answer that has that.

Second one is C. Parallel lines have the same slope, and there is only one answer with the same slope ( -1/2 )

Vertical lines go up and down, so that means that every point has the same X value. Since the point is going through X=-3,Y=6, the correct answer is D, x=-3.

Answer 2

First one: For perpendicular, invert the slope and change the sign. The slope is 4/3, so the answer slope is -3/4. Only one answer has that slope, B. The rest of the info is to trip you up.

Second one: For parallel, the slopes have to be the same. The slope is -1/2, and only only answer has that slope, C. The rest of the info is to trip you up.

The third one is straight forward. A quick, simple graph reveals that x is always -3, regardless of y. So x= -3, or D. Vertical lines are always x = a number. Horizontal lines are always y = a number.

Answer 3

For perpendicular line check m1* m2 = -1 where m is the slope

y = 4/3 x + 4 m = 4/3 so perpendicular line must have slope of -3/4

so answer is B

For parallel lines, slope must be the same

so answer is C

and for a vertical line it must be x = b
and if it pass through -3 then x = -3 Answer D