Regarding equation of the line and perpendicular

Question

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 

Answer 1

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!

Answer 2

 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.     

 

 

 

 

Answer 3

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

:)

Answer 4

"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.

 

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"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.