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y=3x-1;y=3;x-3y=6;x=6

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First, I am going to solve all of the lines that I can to slope intercept form:

1.  y = 3x - 1 (solved to slope intercept form already)


2.  y = 3

y = 0x + 3 (rewritten in slope intercept form)

 

3.  x - 3y = 6

-3y = -x + 6 (subtract x from each side)

y = (1/3)x - 2 (dived each side by -3 to solve to slope intercept form

 

4.  x = 6

0 = -x + 6

0y = -x + 6 (cannot solve to actual slope-intercept form)

 

Since 1 and 3 have the same sign on x (both are positive), they cannot be perpendicular to each other.

 

Line 2 is horizontal (slope is 0).  Line 4 is vertical (the slope is undefined because you have to divide by 0 to find it).

Horizontal and vertical lines are perpendicular, so lines 2 and 4 are perpendicular.