Question

y=9x+3 and x+9y=4 perpdencular or barrel

Answer 1

If we write a line in the form

$y=mx+q$

Then the coefficient m is the slope of the line.

Two lines $y=mx+q$ and $y=m'x+q'$ are:

• Parallel if $m=m'$
• Perpendicular if $mm'=-1$

The first line is already in the required form: $y=9x+3$. We deduce that its slope is 9.

Let's rewrite the second line in the required form:

$x+9y=4 \iff 9y=-x+4 \iff y = -\dfrac{x}{9}+\dfrac{4}{9}$

So, its slope is -1/9.

9 and -1/9 are obviously not equal, so the lines are not parallel.

But their product is -1, which means that the lines are perpendicular.