Question 88085
Perpendicular lines have slopes which are negative reciprocals of each other.
So, the first step is to find the slope of the given line:
{{{2x-3y=6}}}
Put it in y=mx+b form:
{{{-3y=-2x+6}}}
{{{y=2x/3-2}}}
Now, you can just read off the slope from the equation. It is 2/3.
So the line L, since it is perpendicular to this line, will have a slope
{{{m=-3/2}}}
which is the negative reciprocal of 2/3.
They are already giving you the Y-intercept, which is 2. So you are ready to write out the equation of the line:
{{{highlight(L=-3x/2+2)}}}
Good Luck,
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