To start lets convert that equation into slope-intercept form (recall: y=mx+b), both so we know the y-intercept (b) we need to match, and also know the slope (m - which we need to be perpendicular to).
Basic Algebra:
3X + 2Y+ 8 = 0
2Y = -3X -8
Divide both sides by 2.
Y = -(3/2)X - 4
Easy Mistake:
Perpendicular does not mean the same as reciprocal as a warning, some confuse the terms. It's incorrect because there is also a sign change. Many people take the reciprocal and forget to swap signs.
Just remember - 'perpendicular is opposite and reciprocal'. Flows off the tongue doesn't it? Maybe not, but make sure it sticks in your brain like honey holding it because a common forgetful error by some.
Find New Slope:
To find the perpendicular line, find the line with the opposite AND reciprocal slope. Since in the above, slope is -3/2, the opposite and reciprocal is 2/3. Note the sign change. So the slope (m) of the perpendicular line is m=2/3.
We know the y-intercept of the original was -4, and the y-intercept must match for the new line. In other words, it is a point in common between the two. We could therefore safely change the slope and be done with the new equation being: Y = (2/3)X -4.
If you are ever unsure you can double check by plugging both equations into a graphing calculator when done such as the free one found at Desmos.com, and examining the results.
Keep on Going!
