11. y = -3x + 6 and y = 1/3 x -8 (perpendicular)
12. y = 5/4 x + 1 and y = 5/4 x - 7 (parallel)
13. 3x + 2y = 6 and y = -3/2 x + 5 (parallel)
14. 3y = 4x + 15 and 9x + 12y = 12 (perpendicular)
15. 10x - 2y = 16 and x + 5y = -20 (perpendicular)
For two equations to be parallel, the slope has to be the same
For two equations to be perpendicular, the product of their slopes must be equal to -1
The equation of a line is the slope-intercept form is:
y = mx + c
where m is the slope and c is the intercept
11) y = -3x + 6 and y = 1/3 x -8
The equations are perpendicular because -3 x 1/3 = -1
12) y = 5/4 x + 1 and y = 5/4 x - 7
The two lines are parallel because they both have a slope of 5/4
13) 3x + 2y = 6 and y = -3/2 x + 5
The equation 3x + 2y = 6 can be re-written as y = -3/2 x + 3
Therefore, the two equations are parallel since they have the same slope of -3/2
14) 3y = 4x + 15 and 9x + 12y = 12
3y = 4x + 15 can be re-written as y = 4/3 x + 5
9x + 12y = 12 can be re-written as y = -3/4 x + 1
The two lines are perpendicular because -3/4 x 4/3 = -1
15) 10x - 2y = 16 and x + 5y = -20
10x - 2y = 16 can be re-written as y = 5x - 8
x + 5y = -20 can be re-written as y = -1/5 x - 4
Both equations are perpendicular since -1/5 x 5 = -1
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