Question

helper will get a medal !!
Write the standard form of the line that passes through the point (-2, 4) and is parallel to x - 2y = 6

Answer 1

Do you know standard form ?

Answer 2

yes ax+by=c

Answer 3

Have you maybe tried plugging in the numbers

Answer 4

plugging in the points?

Answer 5

Plugging in the points just gives you a number. That won't help you. The purpose of the equation provided is to show you the slope of the parallel line. Parallel lines have the EXACT same slope.
So,
-rearrange the given equation, identify the slope (it is the number that ends up in front for the x)
-use this formula \[y-y _{1}=m(x-x _{1})\]
Where y sub 1 and x sub 1 are your provided points (-2, 4)
-Rearrange into standard form\[y=mx+b\]

Answer 6

And m is your slope.

Answer 7

yeah do you know like conceptually what parallel means? it means that the two lines never intersect which is that they must have the same slope.

Answer 8

yes, but it's just the equation im having trouble finding

Answer 9

Did the above information give you what you needed or are you having trouble rearranging it?

Answer 10

im having trouble reearranging

Answer 11

I will use the provided equation to show you an example:
x-2y=6
Since we need the equation to be form y=mx+b
We subtract x from both sides
x(-x)-2y=6-x
x on the left cancels out
-2y=6-x
we need y alone, so we divide both sides by -2 (or multiply by the reciprocal, same thing)
-2y/-2=(6-x)/-2
the -2 on the left cancels out bc anything divided by itself is 1
y=(6-x)/-2
But you want the slope so you only care about the number in front of the x, so you will want to break it up. \[\frac{ 6-x }{ -2 }\]
\[\frac{ 6 }{ -2 } - \frac{ x }{ -2 }\]
which is the same as
\[-3+\frac{ -x }{ -2 }\]
cancel out the negatives and treat the remaining number as a coefficient
\[-3+\frac{ 1 }{ 2 }x\]
Your slope is the number that remains in front of the x.

Answer 12

All those equation have y=
I got lazy, sorry.

Answer 13

its okay haha i got it now

Answer 14

thank you!

Answer 15

^__^ Excellent

Answer 16

Alternative way without finding slope:

If we need a line parallel to another given in standard form Ax+By=C, and the new line has to pass through a given point P(x0,y0).
The new line in standard form is given by
Ax+By=k
where
k=A(x0)+B(y0), in other words, the new line is
\(Ax+By=A(x0)+B(x0)\)

Say given a line L1: x-2y=6, need a line L2 parallel to L1 and through (-2,4),
L2:
Ax+By=A(x0) +B(y0), where (x0,y0)=(-2,4)
x-2y=1(-2)-2(-4)=-10
So the required line is L2: x-2y=-10