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)

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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)   (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 (,) and (,)


Start with the slope formula (note: (,) is the first point (,) and (,) is the second point (,))


Plug in ,,, (these are the coordinates of given points)


Subtract the terms in the numerator to get . Subtract the terms in the denominator to get




Reduce



So the slope is







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




------Point-Slope Formula------
where is the slope, and (,) is one of the given points


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


Plug in , , and (these values are given)



Rewrite as



Distribute


Multiply and to get . Now reduce to get

Subtract from both sides to isolate y


Combine like terms and to get

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Answer:



So the equation of the line which goes through the points (,) and (,) is:


The equation is now in form (which is slope-intercept form) where the slope is and the y-intercept is


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


Graph of through the points (,) and (,)


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:
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
Answer by scott8148(6628)   (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
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