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nike23 · Aug 5, 2007, 07:45 PM

Simplify:
$(-y^{-5})^5(y^{-2}p^{-2})^3$
for that i got
$-y^{-25}y^{-6}p^{-6}$
then what do i do? Do i put all of it under 1? And is the combination this?
$-y^{-19}p^{-6}$ ?

$\frac{(-4h^3v^6)^3(6h^4v^3)}{3h^5}$
for that one i ended up with:
$\frac{-64h^9v^18(6h^4v^3)}{3h^5}$
is this correct and what do i do with the bottom part?

Lines:

I have no idea how to do these type of questions. If you can give an example that would be helpful. I will use those examples as a guide and do them on my own. If they are wrong please explain to me how and why they are wrong. Thank you.

Write an equation of the line that is:
parallel to the line 6x-3y=15 and that passes through the origin
" " y=x+12 and that has the same y-intercept as the line y=2x-9
" " y=(-.75)x and that has the same y-intercept as the line 8y=3x+16

perpendicular to the line y=x-4 and has a y-intercept of 6
" " 5y-3x=25 and that passes through the origin
" " 3y+x=9 and has an x-intercept of 9

galactus · Aug 6, 2007, 04:07 AM

Write an equation of the line that is:
parallel to the line y=4x+9 and has a y-intercept of 3

Here's the first one. Since the lines are parallel, they have the same slope, 4.

It's y intercept is 3. So, with y=mx+b you have y=4x+3

That's it.

With y=mx+b, m is the slope and b is the y-intercept.

If lines are perpendicular, then the line's slope is the negative reciprocal of the other line.

For instance, if a line has slope 2, then the line perpendicular will have slope -1/2.

nike23 · Aug 6, 2007, 06:05 AM

Wow, thanks. That was pretty simple. But how do I do it if the equation is different like: y+2x=4? And I don't really understand how to work with perpendicular... can u explain it to me? Thanks ;)

galactus · Aug 6, 2007, 06:21 AM

If it's in the form y+2x=4, then just solve for y. It'll then be in the y=mx+b form.

I will do one of your perpendicular problems and then you try the others. Okey-doke?

Perp. to 4y-8x=12 and passes through (3,9).

Solve the given equation for y and get $y=\frac{8x+12}{4}=2x+3$

We see the slope is 2, so the perp. Line must have slope -1/2 (negative reciprocal of 2).

Since it passes through (3,9), we use our y=mx+b and solve for b.

x=3 and y=9

$9=\frac{-1}{2}(3)+b$

$b=\frac{21}{2}$

Therefore, the line equation is $y=\frac{-1}{2}x+\frac{21}{2}$

That's it.

nike23 · Aug 6, 2007, 06:43 AM

for 6x-3y=15 and that passes through the origin, i got: $y=\frac{3x}{5}+5$ i don't know how to do the negative reciprocal for this one would it be:
$\frac{-1}{3}x$ ?

galactus · Aug 6, 2007, 11:17 AM

You haven't learned what a reciprocal is? It's 1 divided by the number.
For the last problem you posted, the negative reciprocal is -1/2, not 3/5. Just turn the fraction upside down. Consequently, you're solution is incorrect.
If you solve 6x-3y=15 for y, you get y=2x-5. The slope is 2.

Think about it. If a line is perpendicular to another line, then it has opposite slope.

What is the opposite of 2? -1/2. The negative reciprocal.