Answer :
Let's isolate the variable y.
6x+5y = 8
5y = -6x+8
y = (-6x+8)/5
y = (-6/5)x + 8/5
The result is in slope-intercept form y = mx+b
- m = -6/5 = slope
- b = 8/5 = y intercept
Recall these key facts:
- Parallel lines have equal slopes but different y intercepts.
- Perpendicular lines have negative reciprocal slopes (the y intercepts may be the same or may be different).
Fact 1 will mean that the slope of any parallel line to 6x+5y = 8 is m = -6/5
Meanwhile, fact 2 will mean we flip the fraction (aka reciprocal) and flip the sign from negative to positive. The -6/5 becomes 5/6 which is the perpendicular slope. Notice the original slope and perpendicular slope multiply to -1. This applies to any pair of perpendicular lines as long as neither line is vertical nor horizontal.
I recommend that you stick to fraction form since the numerator and denominator of the slope fraction describe rise and run respectively.
slope = rise/run
rise = how far you move up or down
run = how far you move to the right
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Answers:
- Parallel slope = -6/5
- Perpendicular slope = 5/6
