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Write the equation of a line that is parallel to the line 2x - 4y = 8 and goes through the point (3,0).

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So because this line is parallel to this right over here.

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it is parallel,

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that just means that it has the exact same slope.

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So we're essentially saying find the equation of a line that has the same slope as this line

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and goes through this point.

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So first, let's figure out what the slope of this line is

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and the easiest way to do that is to put this in kind of slope, y intercept form.

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So we have 2x - 4y = 8.

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We want to solve for y.

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We want this to be in the form y = mx + b.

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So let's subtract 2x from both sides

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so we can isolate the y's on the left.

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So that cancels out and we have

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-4y = -2x + 8

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And I'm writing the -2x first just because that gets us closer to the mx + b form.

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Now we can divide both sides of this equation by -4

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so we can isolate the y.

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So we divide everything by -4.

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and the left-hand side, we just have a

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y is equal to (a -2 divided by -4 is 1/2)

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so y is equal to 1/2x (and then 8 divided by -4 is -2)

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so we could write plus -2 or we could just write minus 2.

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So we just rewrote this line over here

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but because we wrote it in mx + b form we now know its slope.

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The slope of this line is 1/2;

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that right there is the slope.

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so the equation of the line that we care about it is going to have the same slope.

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It's going to have the form y is equal to 1/2x plus some y intercept.

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It's not exactly this line,

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b is going to be different than this -2 here,

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but it's going to have the same slope.

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They're going to intersect the y axis in a different place but theyr'e going to be parallel to each other.

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So now we need to figure out how to figure out b.

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And to do that we have this information right over here.

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On this line, the one we care about, when x is 3, y is 0.

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Or we could say that 0 = 1/2 * 3 + b.

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We just have to find a b that sets up this equation

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so that when x is equal to 3, y is equal to 0.

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So we get 0 = 3/2 + b,

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subtract 3/2 from both sides,

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and we get -3/2 = b,

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or b = -3/2

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So we have the equation for our line that is now parallel to this equation

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and goes through the point (3,0).

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It is y is equal to (it has the same slope as this guy up here)

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1/2x and now we know it's y intercept, -3/2,

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and we are done.

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And, actually, if you're interested you could graph these two and see that they're parallel.

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So if you were to graph these,

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I'll do a very rough graph very fast,

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so this is my y axis,

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this is my x axis.

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This line up here, (I'll do it in blue),

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which is the same thing as this line right over here,

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I just algebraically manipulated it

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has a y intercept at -2 and has a slope of 1/2

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so that means that for every one it goes over, it only goes a half up

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or for every 2 it goes over it only goes 1 up.

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So it's going to look something like this

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I'll try my best to draw it.

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It's going to look something like that.

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And so this line over here,

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it's y intercept is at -3/2

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and -3/2 is the same thing as -1 1/2,

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so it's going to be right above it and it has the exact same slope, so it's going to be right above it and so it would look like that.

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They're parallel but they're different lines because they have different y intercepts.