Find the real number a for which the lines −4x+ 3y = 7 and ax− 2y = 4 will be perpendicular.

Answer 1

3 y = 4 x + 7
y = (4/3) x + 7/3
slope is (4/3)
slope of perpendicular = -3/4

so now look at second line, has to have m = slope = -3/4

2 y = a x - 4
y = (a/2) x - 2
so
-3/4 = a/2
a = -3/2

Answer 2

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