SOLUTION: I need a refresher on how to do these types of problems. You dont have to show me the exact answer just maybe an example of a similar problem. 1. Write an equation parallel to 3x

Algebra ->  Linear-equations -> SOLUTION: I need a refresher on how to do these types of problems. You dont have to show me the exact answer just maybe an example of a similar problem. 1. Write an equation parallel to 3x       Log On


   

Question 339008: I need a refresher on how to do these types of problems. You dont have to show me the exact answer just maybe an example of a similar problem.
1. Write an equation parallel to 3x + 6y = -12 going through (4,-2) and graph.
2. Write an equation going through (3,5) and graph.
Found 2 solutions by jim_thompson5910, josmiceli:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first one to get you started. Please only post one problem at a time. Thanks.



3x%2B6y=-12 Start with the given equation.


6y=-12-3x Subtract 3x from both sides.


6y=-3x-12 Rearrange the terms.


y=%28-3x-12%29%2F%286%29 Divide both sides by 6 to isolate y.


y=%28%28-3%29%2F%286%29%29x%2B%28-12%29%2F%286%29 Break up the fraction.


y=-%281%2F2%29x-2 Reduce.


We can see that the equation y=-%281%2F2%29x-2 has a slope m=-1%2F2 and a y-intercept b=-2.


Since parallel lines have equal slopes, this means that we know that the slope of the unknown parallel line is m=-1%2F2.
Now let's use the point slope formula to find the equation of the parallel line by plugging in the slope m=-1%2F2 and the coordinates of the given point .


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y--2=%28-1%2F2%29%28x-4%29 Plug in m=-1%2F2, x%5B1%5D=4, and y%5B1%5D=-2


y%2B2=%28-1%2F2%29%28x-4%29 Rewrite y--2 as y%2B2


y%2B2=%28-1%2F2%29x%2B%28-1%2F2%29%28-4%29 Distribute


y%2B2=%28-1%2F2%29x%2B2 Multiply


y=%28-1%2F2%29x%2B2-2 Subtract 2 from both sides.


y=%28-1%2F2%29x%2B0 Combine like terms.


y=%28-1%2F2%29x Remove the trailing zero


So the equation of the line parallel to 3x%2B6y=-12 that goes through the point is y=%28-1%2F2%29x.


Here's a graph to visually verify our answer:
Graph of the original equation y=-%281%2F2%29x-2 (red) and the parallel line y=%28-1%2F2%29x (green) through the point .


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website.

Jim

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1) You have to get the given equation into
the form y+=+mx+%2B+b, where m is the slope
Any line parallel to the given line
will have the same slope.
3x+%2B+6y+=+-12
6y+=+-3x+-+12
y+=+-%281%2F2%29%2Ax+-+2
m+=+-1%2F2
Now I know the general form I want is
y+=+-%281%2F2%29%2Ax+%2B+b
Now plug in (4,-2) to find b
-2+=+-%281%2F2%29%2A4+%2B+b
b+=+-2+%2B+2
b+=+0
The solution is y+=+-%281%2F2%29%2Ax
(2)
Start with the general form
y+=+mx+%2B+b
From the given info, m can be anything, so I pick m+=+1
Given: (3,5)
5+=+1%2A3+%2B+b
b+=+2
y+=+x+%2B+2 is one possible answer