Search 83,337 tutors
FIND TUTORS
Ask a question
0 0

Regarding equation of the line and perpendicular

I have the following math problem:
 
Write the equation of the line in the standard form. Containing (9,8) and perpendicular to 3x-4y-5=0.
 
I am so lost! I have no idea where to begin. 
 
Also, previously I had asked the following question:
 
Find an equation of the line containing the given points (1,3) and -3,-7). Express your answer in slope-intercept form. 
 
Very nice tutors on this site helped me with this problem and I watched some videos that were helpful. Here's what I came up with as my answer:
 
y=2.5x+.5 
 
Did I totally butcher this problem? Did I do it right or am I completely off? Please help 
Tutors, please sign in to answer this question.

4 Answers

Hi Grace;
Write the equation of the line in the standard form. Containing (9,8) and perpendicular to 3x-4y-5=0.
 
Standard form is...
Ax+By=C, neither A nor B equal zero, and A is greater than zero.
This can also be written as...
Ax+By-C=0
3x-4y-5=0
slope is -A/B
slope is -(3/-4)
A negative of a negative is positive.
slope is 3/4.
The slope of the perpendicular line is...
-4/3
-A/B
-(-4/3)
A=4, B=3
Ax+By-C=0
4x+3y-C=0
Let's use the one point provided (9,8) to establish C...
[(4)(9)]+[(3)(8)]-C=0
36+24-C=0
60-C=0
60=C
4x+3y-60=0
 
 
Find an equation of the line containing the given points (1,3) and -3,-7). Express your answer in slope-intercept form.

Slope is the change-of-y divided by the change-of-x.
(y-y1)/(x-x1)
You can label either point 1.  As long as you are consistent in that you denote the 1 to the x and y of the same point, it will not make a difference.
(3--7)/(1--3)
Subtracting a negative number is the same as adding a positive number...
(3+7)/(1+3)
10/4
2.5
y=mx+b
y=2.5x+b
3=[(2.5)(1)]+b
3=2.5+b
0.5=b
 
y=2.5x+.5
THAT IS YOUR RESULT!  YOU CAN DO IT!
 L1 : 3X - 4y - 5 =0
 
           Y = 3/4 X -5/4
 
  Find L 2 :   Y = m X + b  that is Perpendicular  to  L1 passes thorough (9, 8)
 
           Y = -4/3 X + b
 
            8 = -4/3( 9) + b
 
           b = 12+8 = 20
 
      L1 :   Y = -4/3 X + 20
 
       or       4X +3y = 60
     This is simple way of using the theorems . The slope of the 2 perpendicular line are negative reciprocal of each other. Coordinates of any point on the line have to satsify the  equation.     
 
 
 
 
From given line equation 3x - 4y -5 = 0 find out slope
 
Convert this equation to slope intercept form y = mx + b where m is slope
 
therefore given line equation  y = 3/4x - 5/4  so slop is 3/4
 
Slope of line perpendicular to it would be - 4/3
 
Therefore standard equatio of new line is y = -4/3x + b
To find y intercept b substitute x=9 and y=8 since line passes through (9,8)
8 = (-4/3)x9  + b
b = 20 
 
Therefore standard equation of new line is y = -4/3x + 20
:)
"Write the equation of the line in standard form containing (9,8) and perpendicular to 3x-4y-5=0."
 
First we need the slope of 3x-4y-5=0. Solve for y:
3x - 5 = 4y
y = (3/4)x - 5/4
 
The line we want will be perpendicular so the slope we want is -4/3.
 
Now we have a point on our line, (9,8), and it's slope, -4/3.
 
Using Point-Slope Form:
 
y - 8 = (-4/3)(x - 9)
 
Multiply both sides by 3 and distribute on the right:
 
3y - 24 = -4x + 36
+4x+24=+4x+24
4x + 3y = 60 is the equation we want.
 
-----
 
"Find an equation of the line containing the given points (1,3) and (-3,-7). Express your answer in slope-intercept form."
 
Your answer equation, y=2.5x+.5, is in the right form. Let's check that it contains the given points:
 
(1,3):
3 =? 2.5(1)+.5
3 = 3 √
 
(-3,-7):
-7 =? 2.5(-3)+.5
-7 =? -7.5+.5
-7 = -7 √
 
So your equation is correct.