SOLUTION: write the equation of the line which has y-intercept (0,5)and is perpendicular to the line with equation y= -3x+1. I dont understand what they are asking. Please help.

Algebra ->  Coordinate-system -> SOLUTION: write the equation of the line which has y-intercept (0,5)and is perpendicular to the line with equation y= -3x+1. I dont understand what they are asking. Please help.      Log On


   

Question 110440: write the equation of the line which has y-intercept (0,5)and is perpendicular to the line with equation y= -3x+1.
I dont understand what they are asking. Please help.
Found 2 solutions by jim_thompson5910, checkley71:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line


Remember, any two perpendicular lines are negative reciprocals of each other. So if you're given the slope of -3, you can find the perpendicular slope by this formula:

m%5Bp%5D=-1%2Fm where m%5Bp%5D is the perpendicular slope


m%5Bp%5D=-1%2F%28-3%2F1%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%281%2F-3%29 When you divide fractions, you multiply the first fraction (which is really 1%2F1) by the reciprocal of the second



m%5Bp%5D=1%2F3 Multiply the fractions.


So the perpendicular slope is 1%2F3



So now we know the slope of the unknown line is 1%2F3 (its the negative reciprocal of -3 from the line y=-3%2Ax%2B1). Also since the unknown line goes through (0,5), 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 m is the slope and (x%5B1%5D,y%5B1%5D) is the given point



y-5=%281%2F3%29%2A%28x-0%29 Plug in m=1%2F3, x%5B1%5D=0, and y%5B1%5D=5



y-5=%281%2F3%29%2Ax-%281%2F3%29%280%29 Distribute 1%2F3



y-5=%281%2F3%29%2Ax-0%2F3 Multiply



y=%281%2F3%29%2Ax-0%2F3%2B5Add 5 to both sides to isolate y

y=%281%2F3%29%2Ax-0%2F3%2B15%2F3 Make into equivalent fractions with equal denominators



y=%281%2F3%29%2Ax%2B15%2F3 Combine the fractions



y=%281%2F3%29%2Ax%2B5 Reduce any fractions

So the equation of the line that is perpendicular to y=-3%2Ax%2B1 and goes through (0,5) is y=%281%2F3%29%2Ax%2B5


So here are the graphs of the equations y=-3%2Ax%2B1 and y=%281%2F3%29%2Ax%2B5




graph of the given equation y=-3%2Ax%2B1 (red) and graph of the line y=%281%2F3%29%2Ax%2B5(green) that is perpendicular to the given graph and goes through (0,5)

Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
Y=-3X+1 (RED LINE)HAS A SLOPE OF -3 & A Y INTERCEPT OF 1.
FOR A PERPENDICULAR LINE TO THIS LINE IT HAS TO HAVE A SLOPE=1/3.
NOW REPLACE THE X & Y VALUES IN THE LINE EQUATION[Y=mX+b] WITH THE SLOPE OF 1/3 & THE (X,Y) VALUES (0,5) & SOLVE FOR THE Y INTERCEPT.
5=1/3*0+b
b=5
SO WE HAVE THE LINE EQUATION WITH A SLOPE OF 1/3 & PASSING THROUGH(0,5):
Y=X/3+5 (GREEN LINE)
+graph%28+300%2C+200%2C+-16%2C+5%2C+-6%2C+10%2C+y+=+-3x+%2B1%2C+y+=+x%2F3+%2B5%29+ (graph 300x200 pixels, x from -16 to 5, y from -6 to 10, of TWO functions y = -3x +1 and y = x/3 +5).