Question

Tell whether the lines for each pair of equations is parallel, perpandicular, or neither.

1. Y=-3x+7 and -2x+6y=3

2. Y= -1/4x+10 and -2x+8y=6

Answer 1

y = -3x + 7 -- slope here is -3
-2x + 6y = 3 (change to slope intercept form)
6y = 2x + 3
y = 2/6x + 3/6
y = 1/3x + 1/2 -- slope here is 1/3
These lines are perpendicular because the lines have negative reciprocal slopes. To find the negative reciprocal of a slope, just " flip " the slope and change the sign. The negative reciprocal of -3 is 1/3 (you see how I flipped the slope and changed the sign).
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y = -1/4x + 10 -- slope here is -1/4
-2x + 8y = 6 (change to slope intercept form)
8y = 2x + 6
y = 2/8x + 6/8
y = 1/4x + 3/4 -- slope here is 1/4
These lines are neither perpendicular or parallel.

Parallel lines will have the same slope and perpendicular lines will have negative reciprocal slopes.