Algebra II help?

[imabrat]

I need help, and I asked the teacher but she didn't really help much. Plus she hates me so that doesn't help either.

I don't understand "using the slope relationship for perpendicular lines" at all.
The example problem in the book goes like this:

points (3, 5), perpendicular to 2x + 5y = 4
y = mx+b
5 = 5/2 (3) t b
5 = 15/2 + b
b = -5/2

HOW IN THE HECK DID THEY GET B!? I'm soooooooo lost - I don't understand this at all.

 

[CowboyErin]

I need help, and I asked the teacher but she didn't really help much. Plus she hates me so that doesn't help either.

I don't understand "using the slope relationship for perpendicular lines" at all.
The example problem in the book goes like this:

points (3, 5), perpendicular to 2x + 5y = 4
y = mx+b
5 = 5/2 (3) t b
5 = 15/2 + b
b = -5/2

HOW IN THE HECK DID THEY GET B!? I'm soooooooo lost - I don't understand this at all.

To get b, you plug in the points for x and y. 3 would be the x, and 5 is the y (x,y). Then you just solve it like you would any equation to get the answer.

5= 5/2(3) +b
5= 15/2 + b

Then you subract the 15/2 from both sides to get:

- 5/2= b.

I don't know if that helped any. If I need to, I'll write it down my work and scan it, since I can't really type what's needed on the computer.

Sorry if that just confused you more xP

 

[Sparx]

I need help, and I asked the teacher but she didn't really help much. Plus she hates me so that doesn't help either.

I don't understand "using the slope relationship for perpendicular lines" at all.
The example problem in the book goes like this:

points (3, 5), perpendicular to 2x + 5y = 4
y = mx+b
5 = 5/2 (3) t b
5 = 15/2 + b
b = -5/2

HOW IN THE HECK DID THEY GET B!? I'm soooooooo lost - I don't understand this at all.

you plug in the x and y in the point (3,5) to get the slope. (b=slope) does that make sense?

 

[My Wild Love]

Hope this kinda sorta helps?

B is the Y intercept not the slope I believe? It is where the line crosses on the Y axis.

Edit: You might need to convert 2x + 5y = 4 into slope intercept form so it will be easier to understand. It should be "Y= 4/5 - 2X" Haha I'm not sure though... Sorry.

 

[BabyPiglet]

Yes, 'b' is the y-intercept, 'm' is the slope.

 

[princess.chell]

Okie dokie, so, first you need to know that the slope of a line (lets call this line A for a second) perpendicular to another (lets call this line B for a second) is the opposite reciprocal of the other line. So if line A's slope is 2, line B's slope is -1/2. Got that?

From there you take the equation you have 2x+5y=4 and put it in slope intercept form (y=mx+b). So that get's you y=4/5+(2/5)x.
So the slope of that line is +2/5 meaning the slope of the line perpendicular is -5/2.
So know you can plug that into a new slope intercept equation so it reads y=(-5/2)x+b.
They give x and y coordinates so plug those in too. Now you have 5=(-5/2)(3)+b
Solve for b.
5=(-15/2)+b
b=-5/2 or -2.5

Hope that helps =)

 

[WDWtraveler27]

bahaha its like your all speaking chinese xD

 

[taylor3297]

Okie dokie, so, first you need to know that the slope of a line (lets call this line A for a second) perpendicular to another (lets call this line B for a second) is the opposite reciprocal of the other line. So if line A's slope is 2, line B's slope is -1/2. Got that?

From there you take the equation you have 2x+5y=4 and put it in slope intercept form (y=mx+b). So that get's you y=4/5+(2/5)x.
So the slope of that line is +2/5 meaning the slope of the line perpendicular is -5/2.
So know you can plug that into a new slope intercept equation so it reads y=(-5/2)x+b.
They give x and y coordinates so plug those in too. Now you have 5=(-5/2)(3)+b
Solve for b.
5=(-15/2)+b
b=-5/2 or -2.5

Hope that helps =)

I used to teach math and this explanation is great!

 

[imabrat]

Okie dokie, so, first you need to know that the slope of a line (lets call this line A for a second) perpendicular to another (lets call this line B for a second) is the opposite reciprocal of the other line. So if line A's slope is 2, line B's slope is -1/2. Got that?

From there you take the equation you have 2x+5y=4 and put it in slope intercept form (y=mx+b). So that get's you y=4/5+(2/5)x.
So the slope of that line is +2/5 meaning the slope of the line perpendicular is -5/2.
So know you can plug that into a new slope intercept equation so it reads y=(-5/2)x+b.
They give x and y coordinates so plug those in too. Now you have 5=(-5/2)(3)+b
Solve for b.
5=(-15/2)+b
b=-5/2 or -2.5

Hope that helps =)

Okay, I think I got it. This is a real uestion I have to answer, is this right?

through (1, 6), perpendicular to 3x + 5y = 1
y = mx+b
y = 3/5 + 1/5
y = -3/5x + b
6 = -3/5 (1) + b
b = 5/3

 

[princess.chell]

Okay, I think I got it. This is a real uestion I have to answer, is this right?

through (1, 6), perpendicular to 3x + 5y = 1
y = mx+b
y = 3/5 + 1/5
y = -3/5x + b
6 = -3/5 (1) + b
b = 5/3

Almost. The only part where you went wrong is with the concept of perpendicular slopes. Its a weird concept, but basically is says the slope of line A is the opposite reciprocal (meaning flip the fraction and make it the opposite sign) of the slope of line B when they perpendicular. (Remember if line A's slope is 2 then line B's slope is -1/2. Or if line A's slope is -6/9 line B's slope is 9/6. Or if line A's slope is 1/5 then line B's slope is -5)
So you found the right slope for the equation given. But then you have to "flip" (take the reciprocal of) the slope as well as make it the opposite sign. So you're slope in the bolded part should actually be (-5/3). Replug that back into the step below the bolded part, solve for b again, and you've got it. =)

 

[imabrat]

Almost. The only part where you went wrong is with the concept of perpendicular slopes. Its a weird concept, but basically is says the slope of line A is the opposite reciprocal (meaning flip the fraction and make it the opposite sign) of the slope of line B when they perpendicular. (Remember if line A's slope is 2 then line B's slope is -1/2. Or if line A's slope is -6/9 line B's slope is 9/6. Or if line A's slope is 1/5 then line B's slope is -5)
So you found the right slope for the equation given. But then you have to "flip" (take the reciprocal of) the slope as well as make it the opposite sign. So you're slope in the bolded part should actually be (-5/3). Replug that back into the step below the bolded part, solve for b again, and you've got it. =)

Okay, I think I've got it. Just to make sure, this was the next problem. I did it although I'm not sure if it's correct, but I think it is.

through (-2, 0), perpendicular to 8x - 3y = 7
y = mx+b
y = 8/-3x + 7/-3
y = -8/-3x + b
y = -8/-3 (-2) + b
b = -3/16

I'm fairly certain I messed up the signs. I ALWAYS mess up the signs, with any "form" of algebra.

 

[princess.chell]

Okay, I think I've got it. Just to make sure, this was the next problem. I did it although I'm not sure if it's correct, but I think it is.

through (-2, 0), perpendicular to 8x - 3y = 7
y = mx+b
y = 8/-3x + 7/-3
y= -8/-3x + b
y = -8/-3 (-2) + b
b = -3/16

I'm fairly certain I messed up the signs. I ALWAYS mess up the signs, with any "form" of algebra.

Heheh, you made the same mistake as before. But don't worry, this is a weird concept. I had issues with it at the beginning too and kids in my calc class miss this all the time.
So your work in the underlined part is right. Then the bolded part you need to flip and take the opposite sign. So in the bold your slope should be 3/8 (you have the sign right because you have a negative in both the top and bottom meaning its a positive) since your slope from the underlined part is (-8/3). The only part you're missing is the reciprocal of the slope. You just need to remember both parts of the concept of perpendicular slopes 1) opposite signs (which you have) and 2) taking the reciprocal (flipping the fraction. My calc teacher sings "And they called him flipper" every time we have to take the reciprocal if that helps you remember, like that dolphin movie. I have a weird calc teacher.)