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Answer: y = (4/3)x + 2</h3>
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Explanation:
The given equation is y = (-3/4)x - 2. Comparing it to y = mx+b, the slope is m = -3/4
Flip the fraction and the sign to go from -3/4 to 4/3. This is the perpendicular slope. Multiplying the two slopes gets (-3/4)*(4/3) = -1.
Rule: the original slope and perpendicular slope always multiply to -1, assuming neither line is vertical or horizontal.
We'll use the point (x,y) = (3,6) and the perpendicular slope m = 4/3 to find the y intercept b
y = mx+b
6 = (4/3)(3) + b
6 = 4+b
6-4 = b
2 = b
b = 2
The y = mx+b equation becomes y = (4/3)x + 2 which is the slope intercept form of the perpendicular line.
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Extra info:
If you want to convert to standard form Ax+By = C, then you could do the following steps
y = (4/3)x + 2
3y = 4x + 6 ... multiply everything by 3 to clear out the fraction
3y - 4x = 6
-4x + 3y = 6
4x - 3y = -6 ... multiplying both sides by -1; this is to make A > 0
