SOLUTION: This one really confused me - please help! Write the equation of the line that satisfies the given condition: contains the point (2,6) and is perpendicular to the line 4x-5y=7.

Algebra ->  Coordinate-system -> SOLUTION: This one really confused me - please help! Write the equation of the line that satisfies the given condition: contains the point (2,6) and is perpendicular to the line 4x-5y=7.       Log On


   

Question 82844: This one really confused me - please help!
Write the equation of the line that satisfies the given condition: contains the point (2,6) and is perpendicular to the line 4x-5y=7.
Thank you!
Found 3 solutions by tutorcecilia, funmath, josmiceli:
Answer by tutorcecilia(2152) About Me  (Show Source):
You can put this solution on YOUR website!
Lines that are perpendicular have slopes that are the negative reciprocal of each other:
For example:
if slope #1 = 2, then the perpendicular slope = -1/2
.
Line #1
4x-5y=7 [re-write in the y=mx+b format]
4x-4x-5y=-4x+7
-5y=-4x+7
-5y/-5=-4/-5x+7/-5
y=4/5x-7/5
Slope # 1 = 4/5
.
So, slope of Line #2 =-5/4 [because I flipped 4/5 and multiplied it by (-1)]
y=mx+b [plug-in the values (2, 6) and (m=-5/4) and solve for the b-term]
6=(-5/4)(2)+b
6=-5/2+b
5/2+6=b
17/2=b
Plug-in just the values of the slope and the b-term:
y=-5/4x+17/2

Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Write the equation of the line that satisfies the given condition: contains the point (2,6) and is perpendicular to the line 4x-5y=7.
First, put the equation in slope intercept form:highlight%28y=mx%2Bb%29, where m=slope and b=y-intercept.
4x-5y=7
-4x%2B4x-5y=-4x%2B7
-5y=-4x%2B7
-5y%2F-5y=%28-4%2F-5%29x-7%2F5
y=%284%2F5%29x-7%2F5
y=highlight%284%2F5%29x-7%2F5 The slope of their line is 4/5.
Perpendicular lines have slopes that are negative reciprocals of each other, so our slope, m=-5/4
We can use the point slope formula to find the equation of our line: highlight%28y-y%5B1%5D=m%28x-x%5B1%5D%29%29, m=slope and (x1,y1) is the given point.
m=-5/4 x1=2 and y1=6
y-6=%28-5%2F4%29%28x-2%29
4%28y-6%29=4%28-5%2F4%29%28x-2%29
4y-24=-5%28x-2%29
4y-24=-5x%2B10
4y-24%2B24=-5x%2B10%2B24
4y=-5x%2B34
5x%2B4y=5x-5x%2B34
5x%2B4y=34
Happy Calculating!!!!

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If you have a point and you know the slope, then you have all you need to write the equation of a line.
The point is given.
Whats the slope?
I know that to find a perpendicular to any given line, the slope of
that perpendicular will be m%5Bp%5D+=+-%281%2Fm%29 where m is the slope
of the given line.
So our line has a line intersecting it which is 4x+-+5y+=+7
Put it in the form y+=+mx+%2B+b where m is the slope
4x+-+5y+=+7
-5y+=+-4x+%2B+7
5y+=+4x+-+7
y+=+%284%2F5%29x+-+7%2F5
m%5Bp%5D+=+4%2F5
Go back to m%5Bp%5D+=+-%281%2Fm%29 and find m of the unknown line
4%2F5+=+-%281%2Fm%29
1%2Fm+=+-%284%2F5%29
1+=+-%284%2F5%29m
m+=+-%285%2F4%29
So the unknown line goes through (2,6) and has a slope -%285%2F4%29
Use the point-slope formula which is
m+=+%28y+-+y%5B1%5D%29+%2F+%28x+-+x%5B1%5D%29
-%285%2F4%29+=+%28y+-+6%29+%2F+%28x+-+2%29
-%285%2F4%29%2A%28x+-+2%29+=+y+-+6
-%285%2F4%29x+%2B+5%2F2+=+y+-+6
-5x+%2B+10+=+4y+-+24
4y+=+-5x+%2B+34
y+=+-%285%2F4%29x+%2B+17%2F2 answer
Is the slope -%285%2F4%29? yes
Does it contain the point (2,6)? Find out
y+=+-%285%2F4%29x+%2B+17%2F2
6+=+-%285%2F4%29%2A2+%2B+17%2F2
6+=+-%285%2F2%29+%2B+17%2F2
12+=+-5+%2B+17
12+=+12 yes
The answer must be right