Question

write the equation of the line in standard form containing (9,8) and perpendicular to 3x-4y-5=0

Answer 1

so first you should put the equation into standard form

Answer 2

Using Ax+By=c

Answer 3

?

Answer 4

put your equation in y = mx + b form because we need to find the slope(m)

Answer 5

can you do that ?

Answer 6

Is it -4=3x+5?

Answer 7

3x - 4y - 5 = 0 (put in y = mx + b form) -- get the y term on one side and everything else on the other side
-4y = -3x + 5
y = 3/4x - 5/4

are you still with me or have I lost you ?

Answer 8

Okay so you just add 4 to both sides .

Answer 9

no..
let me start again and I will go step by step
3x - 4y - 5 = 0 --- subtract 3x from both sides
3x - 3x - 4y - 5 = 0 - 3x -- combine like terms
-4y - 5 = -3x -- add 5 to both sides
-4y - 5 + 5 = -3x + 5 -- combine like terms
-4y = -3x + 5 -- divide both sides by -4
y = (-3/-4)x + 5/(-4)
y = 3/4x - 5/4

understand ?

Answer 10

I understand a little. you lost me at step 4....

Answer 11

now that we have it in y = mx + b form......we know that the slope is in the m position.
So our slope of y = 3/4x - 5/4 is 3/4.

But we are looking for a perpendicular line...that means we need the negative reciprocal slope. All that means is " flip " the slope and change the sign. So the new slope is -4/3 (see how I flipped the slope and changed the sign)

now we use y = mx + b...we already know the slope, so we need to find the y intercept(b)
y = mx + b
slope(m) = -4/3
(9,8)..x = 9 and y = 8
now we sub
8 = -4/3(9) + b
8 = - 12 + b
8 + 12 = b
20 = b

so your perpendicular equation is : y = -4/3x + 20

Answer 12

oh...sorry..
whatever you do on one side of the equal sign, you have to do on the other.
3x - 4y - 5 = 0 --- subtract 3x from both sides
-4y - 5 = -3x -- add 5 to both sides
-4y = -3x + 5 -- now divide by -4 on both sides
y = 3/4x - 5/4

where am I losing you ?

Answer 13

oh wait...you need it in standard form Ax + By = C
y = -4/3x + 20 -- multiply everything by 3
3y = -4x + 60 -- add 4x to both sides
4x + 3y = 60 <=== standard form

Answer 14

Is the top info right for the problem or is the last statement you wrote is what I really need?

Answer 15

the top info is just doing the problem...but I didn't realize you needed it in standard form, so the last part was me finishing the problem. The answer you need is : 4x + 3y = 60 -- thats your perpendicular line going through points (9,8)

Answer 16

Okay i have an under standing. Of what you just showed me . But do I really need to do those first steps all the time when I have problems like this?
Mathematics is my weakest subject. Im just trying to get an clear understanding.

Answer 17

yes...unfortunately you do. You have to do the first steps to find the slope. Then, for a perpendicular line, you have to find the negative reciprocal slope. Then you have to do your subbing in the formula y = mx + b to find your line in slope intercept form. And then you can convert it to standard form.