SOLUTION: solve for y in 6x-5y=-5. determine if the line is parallel to y=6/5x+5/9

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Question 115771: solve for y in 6x-5y=-5. determine if the line is parallel to y=6/5x+5/9
Found 2 solutions by edjones, bucky:
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
y=mx+b m=slope
y=6x/5+5/9 m=6/5
If the next equation has the same slope they are parallel.
6x-5y=-5
6x-6x-5y=-6x-5
-5y=-6x-5
-5y/-5=-6x/-5 -5/-5
y=6x/5+1 m=6/5
They are parallel.
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Ed

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
One step at a time. First, solve the equation 6x+-+5y+=+-5 for y:
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Begin by getting rid of the term 6x on the left side so that you just have the term containing
the y alone on the left side. Do this by subtracting 6x from both sides to get:
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-5y+=+-6x+-+5
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You are trying to solve for +y so at this point you may want to change the sign of -5y to +5y.
You can do that by multiplying both sides of the equation (all terms) by -1 to change the
equation to:
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5y+=+6x+%2B+5
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Finally, solve for y by dividing both sides of this equation by 5 ... the multiplier of
y to get:
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y+=+%286%2F5%29%2Ax+%2B+5%2F5+=+%286%2F5%29%2Ax+%2B+1
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Notice that the equation we now have is:
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y+=++%286%2F5%29%2Ax+%2B+1
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and this is in the slope-intercept form:
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y+=+mx+%2B+b
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in which m, the multiplier of x, is the slope of the graph and b is the value on the y-axis
where the graph crosses the y-axis. By comparing your equation with the slope intercept form
you can see that the graph of your equation has a slope of %286%2F5%29 and it crosses the
y-axis at the value of +1 on the y-axis.
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Now look at the other equation you were given ... namely:
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y+=+%286%2F5%29%2Ax+%2B+5%2F9
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Comparing this equation to the slope intercept form you will see that it also has a slope
of 6%2F5 but its graph crosses the y-axis at 5%2F9.
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Now recognize that two graphs having the same slope but different crossing points on the
y-axis are parallel lines that are always separated in vertical distance by an amount equal
to the difference on the y-axis equal to the crossing points. The graph of the two equations
shows this. The "red" graph is the graph of the equation y+=+%286%2F5%29%2Ax+%2B+1 and the green
graph is the graph of the equation y+=+%286%2F5%29%2Ax+%2B+5%2F9
.

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Hope this helps you to understand the problem and shows you that lines given by the two equations
are actually parallel.
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