Question 115771
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 + 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 = (6/5)*x + 5/5 = (6/5)*x + 1}}}
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Notice that the equation we now have is:
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{{{y =  (6/5)*x + 1}}}
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and this is in the slope-intercept form:
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{{{y = mx + 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 {{{(6/5)}}} 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 = (6/5)*x + 5/9}}}
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Comparing this equation to the slope intercept form you will see that it also has a slope 
of {{{6/5}}} but its graph crosses the y-axis at {{{5/9}}}. 
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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 = (6/5)*x + 1}}} and the green
graph is the graph of the equation {{{y = (6/5)*x + 5/9}}}
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{{{graph(800,800,-15,15,-15,15,(6/5)*x + 1,(6/5)*x + 5/9)}}}
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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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