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Question 247823: Please help with the following equation:
Write an equation of the line containing the specified point and parallel to the indicated line (3,-4), 5x-6y=4 I think I need to plug the points 3 and -4 in for x and y and solve but I am confused how to remove them both from the same side of the equation. Thank you for any help!
Found 2 solutions by Alan3354, richwmiller:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Write an equation of the line containing the specified point and parallel to the indicated line (3,-4), 5x-6y=4
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First, find the slope, m, of the line. To do that, put it into slope-intercept form y = mx + b. That means solve for y.
5x-6y=4
y = (5/6)x + something, doesn't matter.
The slope is 5/6
All lines parallel to it have the same slope.
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Use y = mx + b and the point to find b:
-4 = (5/6)*3 + b
b = -13/2
--> y = (5/6)x - 13/2 is parallel and thru the point.
Answer by richwmiller(17219)  (Show Source):
You can put this solution on YOUR website! plug them in and you get
5(x)-6(y)=4
x=3
y=-4
5(3)-6(-4)=4
15+24=4
39=4
but 39 doesn't equal 4
That tells use that the point is not on that line.
But the problem already told us that.
The equation 5x-6y=4 is another line.
We want one that is parallel to that line.
and goes through the point(3,-4) where x=3 and y=-4
solve for y
5x-6y=4
5x=6y+4
subtract 4 from both sides
5x-4=y
y=5x-4
y=mx+b
m is the slope and b is the y intercept
which means that if x=0 then y is b
so 5 is the slope and it goes through (0,-4)
so we want a line of the same slope but goes through (3,-4)
we see that x is three more than (0,-4)
y=mx+b
we know x,y and m
-4=5(3)+b
-4=15+b
subtract 15 from both sides
-19=b
so now we can make the new equation
y=mx+b where m=5 and b=-19
y=5x-19 is a line parallel to the given line and goes through (3,-4)
and has the y intercept (0,-19)
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