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)

Algebra ->  Linear-equations -> 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)      Log On


   

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) 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 (4,-4) and (3,-2)


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 (4,-4) and (x%5B2%5D,y%5B2%5D) is the second point (3,-2))


m=%28-2--4%29%2F%283-4%29 Plug in y%5B2%5D=-2,y%5B1%5D=-4,x%5B2%5D=3,x%5B1%5D=4 (these are the coordinates of given points)


m=+2%2F-1 Subtract the terms in the numerator -2--4 to get 2. Subtract the terms in the denominator 3-4 to get -1




m=-2 Reduce



So the slope is

m=-2





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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--4=%28-2%29%28x-4%29 Plug in m=-2, x%5B1%5D=4, and y%5B1%5D=-4 (these values are given)



y%2B4=%28-2%29%28x-4%29 Rewrite y--4 as y%2B4



y%2B4=-2x%2B%28-2%29%28-4%29 Distribute -2


y%2B4=-2x%2B8 Multiply -2 and -4 to get 8%2F1. Now reduce 8%2F1 to get 8

y=-2x%2B8-4 Subtract 4 from both sides to isolate y


y=-2x%2B4 Combine like terms 8 and -4 to get 4

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Answer:



So the equation of the line which goes through the points (4,-4) and (3,-2) is:y=-2x%2B4


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-2 and the y-intercept is b=4


Notice if we graph the equation y=-2x%2B4 and plot the points (4,-4) and (3,-2), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=-2x%2B4 through the points (4,-4) and (3,-2)


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 (-6,4) and (-7,6)


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 (-6,4) and (x%5B2%5D,y%5B2%5D) is the second point (-7,6))


m=%286-4%29%2F%28-7--6%29 Plug in y%5B2%5D=6,y%5B1%5D=4,x%5B2%5D=-7,x%5B1%5D=-6 (these are the coordinates of given points)


m=+2%2F-1 Subtract the terms in the numerator 6-4 to get 2. Subtract the terms in the denominator -7--6 to get -1




m=-2 Reduce



So the slope is

m=-2





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


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-4=%28-2%29%28x--6%29 Plug in m=-2, x%5B1%5D=-6, and y%5B1%5D=4 (these values are given)



y-4=%28-2%29%28x%2B6%29 Rewrite x--6 as x%2B6



y-4=-2x%2B%28-2%29%286%29 Distribute -2


y-4=-2x-12 Multiply -2 and 6 to get -12%2F1. Now reduce -12%2F1 to get -12

y=-2x-12%2B4 Add 4 to both sides to isolate y


y=-2x-8 Combine like terms -12 and 4 to get -8

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Answer:



So the equation of the line which goes through the points (-6,4) and (-7,6) is:y=-2x-8


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-2 and the y-intercept is b=-8


Notice if we graph the equation y=-2x-8 and plot the points (-6,4) and (-7,6), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=-2x-8 through the points (-6,4) and (-7,6)


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