Question

Determine whether the graphs of the given equations are parallel, perpendicular, or neither.

Y - 4 = 3( x + 2 )

2x + 6y = 10

Answer 1

When the slopes are equal, the two lines are parallel.
When the product of two slopes is -1, then the two lines are perpendicular.
So, y - 4 = 3x + 6 ;
Then, y = 3x + 10 ; the slope of the first line is 3 ;
2x + 6y = 10 ;
Then, 6y = - 2x + 10 ;
y = (-2/6)x + 10/6 ;
Finally, y = (-1/3)x + 5/3; the slope if the second line is -1/3;
Because 3*(-1/3) = -1 the two lines are perpendicular.