SOLUTION: Write an equation of a line pependicular to y= -1/4x +5

Algebra ->  Linear-equations -> SOLUTION: Write an equation of a line pependicular to y= -1/4x +5      Log On


   

Question 121333: Write an equation of a line pependicular to y= -1/4x +5
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
a line pependicular to y=+-1%2F4x+%2B5
recall:
a pependicular lines have the product of slopes equal to -1
or
m* m[1]= -1
given:
y=+-1%2F4x+%2B5........this is a slope-intercept form and the slope m is equal to -1/4

so, we need to find the slope m[1]

m%2Am%5B1%5D+=+-1

%28-1%2F4%29%2Am%5B1%5D+=+-1

m%5B1%5D+=+%28-1%29%2F%28-1%2F4%29

m%5B1%5D+=+%28-1%2F1%29%2F%28-1%2F4%29

m%5B1%5D+=+%28-4%2F-1%29

m[1]= 4

the slope-intercept form will be:
y+=+m%5B1%5Dx+%2B+b
if you assume that b=0, your equation will be:
y+=+4x+
here is the graph:
Solved by pluggable solver: Solve the System of Equations by Graphing


Let's look at the first equation %281%2F4%29x%2By=5



4%28%281%2F4%29x%2By%29=4%285%29 Multiply both sides of the first equation by the LCD 4



1x%2B4y=20 Distribute



---------




So our new system of equations is:


1x%2B4y=20

-4x%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


1x%2B4y=20 Start with the given equation



4y=20-x Subtract +x from both sides



4y=-x%2B20 Rearrange the equation



y=%28-x%2B20%29%2F%284%29 Divide both sides by 4



y=%28-1%2F4%29x%2B%2820%29%2F%284%29 Break up the fraction



y=%28-1%2F4%29x%2B5 Reduce



Now lets graph y=%28-1%2F4%29x%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+%28-1%2F4%29x%2B5%29+ Graph of y=%28-1%2F4%29x%2B5




So let's solve for y on the second equation


-4x%2By=0 Start with the given equation



1y=0%2B4x Add 4+x to both sides



1y=%2B4x%2B0 Rearrange the equation



y=%28%2B4x%2B0%29%2F%281%29 Divide both sides by 1



y=%28%2B4%2F1%29x%2B%280%29%2F%281%29 Break up the fraction



y=4x%2B0 Reduce





Now lets add the graph of y=4x%2B0 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28-1%2F4%29x%2B5%2C4x%2B0%29+ Graph of y=%28-1%2F4%29x%2B5(red) and y=4x%2B0(green)


From the graph, we can see that the two lines intersect at the point (20%2F17,80%2F17) (note: you might have to adjust the window to see the intersection)