**(9,8)**and

**perpendicular**to 3x-4y-5=0.

**y=2.5x+.5**

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:

Did I totally butcher this problem? Did I do it right or am I completely off? Please help

Tutors, sign in to answer this question.

Hi Grace;

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

Slope is the change-of-y divided by the change-of-x.

(y-y_{1})/(x-x_{1})

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

Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...

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.

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