Question 107392
Given the equation:
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-4x - 3y = 6
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The slope-intercept form of this equation will be in the form of:
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y = mx + b
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and in this form, m (the multiplier of x) is the slope and b (the constant) is the y-intercept.
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So to solve the problem you can work the given equation into the slope intercept form.
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Begin by getting rid of the -4x on the left side. Do this by adding +4x to both sides. When
you add +4x to the left side, it cancels the -4x and so on the left side the x-terms 
disappear. On the right side, when you add +4x, the term +4x appears. So by adding +4x to
both sides the given equation becomes:
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-3y = +4x + 6
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Now solve this equation for y by dividing both sides by -3 (the multiplier of y on the
left side. When you do this division (both sides ... all terms) the left side becomes just
y and both terms on the right side are divided by -3.
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{{{y = (4/-3)x + 6/-3 = -(4/3)x - 2}}}
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Therefore the equation is reduced to:
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{{{y = -(4/3)x - 2}}}
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Notice how this compares to the point-slope form. In this equation the multiplier of
x is {{{-(4/3)}}} and the multiplier of x is the slope.  Therefore, the slope of the graph of
the given equation is {{{-(4/3)}}}.  And the constant term on the right side ... which is -2 ...
is the point on the y-axis where the graph crosses the y-axis.
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You can graph {{{y = -(4/3)x-2}}}. This graph is the same as the graph of the original equation
you were given as a problem.  The graph looks like this:
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{{{graph(600,600,-10,10,-10,10, -(4/3)x - 2)}}}
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Hope this helps you to understand the problem.
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