anonymous
  • anonymous
Write an equation of the line containing the given point and parallel to the given line. (-2,8); 7x=5y+6
Mathematics
chestercat
  • chestercat
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shadowfiend
  • shadowfiend
If two lines are parallel, what is the relation between their slopes?
anonymous
  • anonymous
are they equal distance?. i dunno im horrible with math, not one of my strong points
shadowfiend
  • shadowfiend
It's okay :) Two parallel lines have equal slopes. So, y = 3x + 135 y = 3x + 2 Those two are parallel lines, because they the same slope (3). Let's focus on the problem below, since you'll have to use the same technique to get the equation they give you in y = mx + b form here.

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shadowfiend
  • shadowfiend
So now you have 7x = 5y + 6. Since we need the slope, we need to solve for y again.
anonymous
  • anonymous
okay so would we need to subtract 6 from both sides?
shadowfiend
  • shadowfiend
Yep, that's the first step.
anonymous
  • anonymous
-6+7x=5y
anonymous
  • anonymous
or 5y=7x-6
shadowfiend
  • shadowfiend
Right. What's next?
anonymous
  • anonymous
get the y by itself
shadowfiend
  • shadowfiend
Exactly. So since the y is multiplied by 5, how do we get it by itself?
anonymous
  • anonymous
divide
shadowfiend
  • shadowfiend
Right. So we divide each part of the right by 5; what do we get?
anonymous
  • anonymous
y=7/5x-6/5
shadowfiend
  • shadowfiend
Boom! Exactly. So now we know what the slope of a parallel line would have to be. What is it?
anonymous
  • anonymous
7/5
shadowfiend
  • shadowfiend
Right. So now we'll need another equation that looks like: y = 7/5x + b Does that make sense?
anonymous
  • anonymous
yea that does
shadowfiend
  • shadowfiend
Ok, and now they've given us a point that the line goes through, so we can plug in the x and y and solve for b.
anonymous
  • anonymous
okay so 8=7/5(-2)+b
anonymous
  • anonymous
is that right
anonymous
  • anonymous
Absolutely!
anonymous
  • anonymous
So now what do I do?
anonymous
  • anonymous
So we need to figure out what b is, right? How should we do that?
anonymous
  • anonymous
um get b by itself?
anonymous
  • anonymous
Exactly. So what's the first step?
anonymous
  • anonymous
multiply 7/5(-2)
anonymous
  • anonymous
Ok, what does that equal?
anonymous
  • anonymous
-6/5
anonymous
  • anonymous
Not quite. Remember you are multiplying 7/5 by -2. Do you know how to multiply fractions?
anonymous
  • anonymous
not really is it common denominators at all?
anonymous
  • anonymous
That is actually for adding and subtracting. Multiplication is much easier. You are multiplying 7/5 by -2. Remember that -2 is the same as -2/1, which means you have \[\frac{7}{5} \times \frac{-2}{1}\] then you just multiply straight across. What do you get?

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