What is the equation of the line that passes through (4, 2) and is parallel to 3x – 2y = –6?

Question

zepdrix · Answer

So they gave us the equation of a line in `standard form`:
$$\Large\rm 3x-2y=-6$$
If we find the slope we can set up the other line.
Do you know how to get this line into `slope-intercept` form?

anonymous · Answer

no not really

zepdrix · Answer

slope-intercept form looks like this $\Large\rm y=stuff$
Only y on the left side.

So to isolate the y, you need to move all that other junk to the right side.
Subtracting 3x gives us,$$\Large\rm -2y=-6-3x$$Understand that step?

anonymous · Answer

mhmm yep

anonymous · Answer

then your suppose to take 2 away frum both sides to get y by itself?

zepdrix · Answer

Well the negative 2 is `multiplying` y,
so we can't take it away by adding/subtracting right?

anonymous · Answer

nope division

zepdrix · Answer

$$\Large\rm y=\frac{-6-3x}{-2}$$Ok cool.
So you'll need to divide `both` the -6 and -3 by -2.
Can you simplify that right side?

anonymous · Answer

yep into $$\frac{ 3x }{ -2 }$$ ?

zepdrix · Answer

No, those negatives should cancel out, changing it to positive.

zepdrix · Answer

And don't forget about the other term,
the -6 divide -2 gives us 3, yes?

anonymous · Answer

yeah yeah i 4got about taking out the negatives but thanx u've been a real help ...its kinda hard switching from Geometry back to Algebra 1

zepdrix · Answer

Anyway, this only get's you through half of the problem.$$\Large\rm y=3+\frac{3}{2}x$$So you found that your slope is $\Large\rm m=\dfrac{3}{2}$

Since the other line is `parallel` to this one, it means they have the `same slope`.

zepdrix · Answer

So our new line will be,$$\Large\rm y=\frac{3}{2}x+b$$It has a different y-intercept than the line we started with, but the same slope (parallel).

To find the y-intercept, plug in the coordinate pair they gave you, and solve for b.

anonymous · Answer

k thnx