SOLUTION: Find the equations for the following lines and then graph them using any graphing utility Parallel to 6x - 4y + 12 = 0, and passing through the line x = 3 6 times (3)-4y

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Question 298725:
Find the equations for the following lines and then graph them using any graphing utility
Parallel to 6x - 4y + 12 = 0, and passing through the line x = 3
6 times (3)-4y+12=0
18-4y+12=0 y=30/4 or 7.5
30-4y=0
30=4y

6x-4y+12=0 -4y/-4 = 6x+12/-4
4y=6x+12 y=6/-4x + 12 y=1.5x+12
slope = 6/-4 solution (3, 7.5)
So I was able to get this much not sure if it is correct however I am lost when it comes to the graphing and the part of the problem whre it states passing through the line x=3
any help is much appreciated and needed Thank you
Eric
Answer by richwmiller(17219) (Show Source):
You can put this solution on YOUR website!
Please don't yell. We can hear you. We have new batteries in the hearing aids.
HELLO I AM LOST ON THIS PROBLEMI I WAS ABLE TO COME UP WITH PART OF THE ANSWER BUT I AM NOW STUCK. I ALSO HAVE NO CLUE HOW TO GRAPH THIS ANY HELP WOULD BE APPRECIATED.
All Caps is internet yelling.
If it passes through x=3 that means the new line at some time has x=3
the original line has the equation 6x - 4y + 12 = 0
it has a slope of -a/b=-6/-4=3/2
The new line will also have a slope of 3/2
and an x of 3
y=3x/2 is our new line
We are pretty sure it will pass through x=3
But how can we be sure?
The only lines that won't pass through x=3 are parallel with x=3 x=3 has an undefined slope since y never changes.
Our line has a slope of 3/2 so they do intersect.
As a further test we can see if the original line passes through x=3
by plugging in 3 for x in the original equation but it is not necessary.