Answer: Neither
Not parallel, and not perpendicular either.
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How we can determine that answer:
Let's solve for y in the 1st equation.
-3x+4y = 8
4y = 3x+8
y = (3x+8)/4
y = (3x/4) + (8/4)
y = (3/4)x + 2
Compare this to the slope-intercept form y = mx+b
- m = 3/4 = slope
- b = 2 = y intercept
If you solved -4x+3y = -6 for y, then you should get y = (4/3)x - 2. I'll leave the steps for the student to do. The steps will be similar to what's shown above.
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To summarize so far, the slopes of the original equations are 3/4 and 4/3 in that exact order.
The slopes aren't equal, so the lines aren't parallel. Parallel lines occur when the slopes are equal but y intercepts are different. Example: y = 2x+5 and y = 2x+7 are parallel.
The slopes 3/4 and 4/3 do not multiply to -1; this would mean the lines are not perpendicular.
An example pair of perpendicular slopes would be 3/4 and -4/3. Each slope is the negative reciprocal of the other. If one slope is positive, then the other must be negative.
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In conclusion, the final answer is neither
The lines aren't parallel, and they aren't perpendicular either.
Graphing tools like GeoGebra can be helpful to visually confirm the answer.