We get the perpendiculars to a line in standard form by swapping the coefficients on x and y, negating one of them. It's the same idea as the negative reciprocal slope. The constant is determined by other things, so unknown here.
Find the perpendicular to 5y + 2x = 15
They're trying to trick us a bit; for sanity we rewrite our given line in standard form:
2x + 5y = 15
For the perpendicular family we swap the coefficients and negate one. The constant is unknown.
5x - 2y = k
That's standard form; we can rewrite it in slope/intercept form:
2y = 5x - k
y = (5/2)x - k/2
Now let's look at the choices.
Surprisingly we don't see one of these among the choices. They want us to understand one more very important fact. The coefficients in a line equation only matter in ratio. So
5x - 2y = k
is the same line as
10x - 4y = 2k
or
-15x + 6y = -3k
Allowing for this, we see our answer.
Answer: B. 10x-4y=12
