SOLUTION: Using the form y=mx+b,find the equation for ;The line thru the orgin that is perpendicular to the line through (-3,0) and(0,- 3)

Algebra ->  Graphs -> SOLUTION: Using the form y=mx+b,find the equation for ;The line thru the orgin that is perpendicular to the line through (-3,0) and(0,- 3)      Log On


   

Question 99323: Using the form y=mx+b,find the equation for ;The line thru the orgin that is perpendicular to the line through (-3,0) and(0,- 3)
Found 2 solutions by edjones, scott8148:
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (0,-3) and (-3,0)


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula (note: (x%5B1%5D,y%5B1%5D) is the first point (0,-3) and (x%5B2%5D,y%5B2%5D) is the second point (-3,0))


m=%280--3%29%2F%28-3-0%29 Plug in y%5B2%5D=0,y%5B1%5D=-3,x%5B2%5D=-3,x%5B1%5D=0 (these are the coordinates of given points)


m=+3%2F-3 Subtract the terms in the numerator 0--3 to get 3. Subtract the terms in the denominator -3-0 to get -3




m=-1 Reduce



So the slope is

m=-1





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Now let's use the point-slope formula to find the equation of the line:




------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 one of the given points


So lets use the Point-Slope Formula to find the equation of the line


y--3=%28-1%29%28x-0%29 Plug in m=-1, x%5B1%5D=0, and y%5B1%5D=-3 (these values are given)



y%2B3=%28-1%29%28x-0%29 Rewrite y--3 as y%2B3



y%2B3=-x%2B%28-1%29%280%29 Distribute -1


y%2B3=-x%2B0 Multiply -1 and 0 to get 0%2F1. Now reduce 0%2F1 to get 0

y=-x%2B0-3 Subtract 3 from both sides to isolate y


y=-x-3 Combine like terms 0 and -3 to get -3

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Answer:



So the equation of the line which goes through the points (0,-3) and (-3,0) is:y=-x-3


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-1 and the y-intercept is b=-3


Notice if we graph the equation y=-x-3 and plot the points (0,-3) and (-3,0), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=-x-3 through the points (0,-3) and (-3,0)


Notice how the two points lie on the line. This graphically verifies our answer.



y= -x-3 slope=m= -1
slope of a line perpendicular to any line is its negative reciprocal: m=+-1%2Fm%5B1%5D=+-1%2F-1=+1
the origin is point (0,0)
y-y[1]=m(x-x[1])
y-0=1(x-0)
so our equation for the in through the origin perpendicular to our 1st line is y=x
Ed
graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C-x-3%2Cx%29

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
the slope of the first line is (0-(-3))/(-3-0) or -1

the slope of the perpendicular is the negative reciprocal or 1

the perpendicular goes thru (0,0) so the y-intercept is 0

y=x