SOLUTION: Which is the equation for the line perpendicular to y = -5/3x + 11 1/3 and containing P(–2,3)? I know I have to write an equation for a line, but I don't understand what the que

Algebra ->  Graphs -> SOLUTION: Which is the equation for the line perpendicular to y = -5/3x + 11 1/3 and containing P(–2,3)? I know I have to write an equation for a line, but I don't understand what the que      Log On


   

Question 670485: Which is the equation for the line perpendicular to y = -5/3x + 11 1/3 and containing P(–2,3)?
I know I have to write an equation for a line, but I don't understand what the question means by 'contained' ? How do I figure this out?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

y+=+-5%2F3x+%2B+11%281%2F3%29 and
point (-2,3)
'contained' means that given point lie one a line which you are looking equation for
Remember, any two perpendicular lines are negative reciprocals of each other. So if you're given the slope of m=-5%2F3, you can find the perpendicular slope by this formula:
m%5Bp%5D=-1%2Fm where m%5Bp%5D is the perpendicular slope
So plug in the given slope to find the perpendicular slope:

m%5Bp%5D=-1%2F%28-5%2F3%29
m%5Bp%5D=-1%2A3%2F-5
m%5Bp%5D=3%2F5
So the perpendicular slope is 3%2F5


So now we know the slope of the unknown line is 3%2F5 (its the negative reciprocal of -5%2F3 from the line y=-%285%2F3%29x-34%2F3. Also since the unknown line goes through (-2,3), we can find the equation by plugging in this info into the point-slope formula
Point-Slope Formula:
y-y%5B1%5D=m%28x-x%5B1%5D%29+where+%7B%7B%7Bm is the slope and (x[1],y[1]) is the given point


y-3=%283%2F5%29%28x%2B2%29
y-3=%283%2F5%29x%2B%283%2F5%292
y=%283%2F5%29x%2B%286%2F5%29%2B3

y=%283%2F5%29x%2B6%2F5%2B3%2A5%2F5
y=%283%2F5%29x%2B6%2F5%2B15%2F5
y=%283%2F5%29x%2B21%2F5
So the equation of the line that is perpendicular to y=-%285%2F3%29x%2B34%2F3 and goes through (-2,3) is y=%283%2F5%29x%2B21%2F5.