SOLUTION: Find the slope of any line perpendicular to the line through points (0,5) and (-3,-4). I have tried to read and reread this and going over the material, please help. Much appre

Algebra ->  Linear-equations -> SOLUTION: Find the slope of any line perpendicular to the line through points (0,5) and (-3,-4). I have tried to read and reread this and going over the material, please help. Much appre      Log On


   

Question 115901: Find the slope of any line perpendicular to the line through points (0,5) and (-3,-4).
I have tried to read and reread this and going over the material, please help.
Much appreciated for your time,
Barb Neely
Found 2 solutions by Fombitz, MathLover1:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
First step, find the slope of the line that goes through those two points.
The slope of a line given two (x,y) points is :
m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29
m=%28-4-5%29%2F%28-3-0%29
m=%28-9%29%2F%28-3%29
m=3
There is a relationship between the slopes of perpendicular lines.
They are negative reciprocals of each other.
m%5B1%5D=-1%2Fm%5B2%5D or
m%5B1%5D%2Am%5B2%5D=-1
You already know the first slope.
3%2Am%5B2%5D=-1
m%5B2%5D=-1%2F3
The slope of the perpendicular line is -1/3.


Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
first find the equation of the line through points (0,5) and (-3,-4)


Solved by pluggable solver: FIND EQUATION of straight line given 2 points
hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (0, 5) and (x2, y2) = (-3, -4).
Slope a is a+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29+=+%28-4-5%29%2F%28-3-0%29+=+3.
Intercept is found from equation a%2Ax%5B1%5D%2Bb+=+y%5B1%5D, or 3%2A0+%2Bb+=+5. From that,
intercept b is b=y%5B1%5D-a%2Ax%5B1%5D, or b=5-3%2A0+=+5.

y=(3)x + (5)

Your graph:




then find slope of any line perpendicular this line:


perpendicular lines have slopes as negative reciprocals
Since a slope for this line is m%5B1%5D=+3, slope for the line perpendicular to this line will be m%5B2%5D+=+-1%2F3
example line is:
y=-%281%2F3%29x
graph both together:
Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


-3x%2By=5

0333333333333333x%2By=0





In order to graph these equations, we need to solve for y for each equation.




So let's solve for y on the first equation


-3x%2By=5 Start with the given equation



1y=5%2B3x Add 3+x to both sides



1y=%2B3x%2B5 Rearrange the equation



y=%28%2B3x%2B5%29%2F%281%29 Divide both sides by 1



y=%28%2B3%2F1%29x%2B%285%29%2F%281%29 Break up the fraction



y=3x%2B5 Reduce



Now lets graph y=3x%2B5 (note: if you need help with graphing, check out this solver)



+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+3x%2B5%29+ Graph of y=3x%2B5




So let's solve for y on the second equation


0333333333333333x%2By=0 Start with the given equation



1y=0-0333333333333333x Subtract 0333333333333333+x from both sides



1y=-0333333333333333x%2B0 Rearrange the equation



y=%28-0333333333333333x%2B0%29%2F%281%29 Divide both sides by 1



y=%28-0333333333333333%2F1%29x%2B%280%29%2F%281%29 Break up the fraction



y=-333333333333333x%2B0 Reduce





Now lets add the graph of y=-333333333333333x%2B0 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+3x%2B5%2C-333333333333333x%2B0%29+ Graph of y=3x%2B5(red) and y=-333333333333333x%2B0(green)


From the graph, we can see that the two lines intersect at the point (-5%2F333333333333336,555555555555555%2F111111111111112) (note: you might have to adjust the window to see the intersection)