SOLUTION: Determine whether the following pairs of lines are parallel, perpendicular or neither. Line 1 is (4,-4) and (3,-2), Line 2 is (-6,4) and (-7,6)

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Question 102590: Determine whether the following pairs of lines are parallel, perpendicular or neither. Line 1 is (4,-4) and (3,-2), Line 2 is (-6,4) and (-7,6)
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







------------------------------------------------


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

------------------------------------------------------------------------------------------------------------

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.



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







------------------------------------------------


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

Add to both sides to isolate y


Combine like terms and to get

------------------------------------------------------------------------------------------------------------

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=-2x+4
y=-2x-8
.
Since the slope for both equations is the same, -2, they are parallel.
Ed
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