Question 94085
You are given the equation:
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{{{5x - 8y = 16}}}
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and are told to use intercepts to graph the equation.
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The intercepts of a linear equation are the coordinate points where it crosses the y-axis and
where it crosses the x-axis. If you plot these two points, you can get the graph by using a 
straight edge to draw a line that extends through these two points and beyond.
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The coordinate point on the y-axis will have an x-value of what?  When you think about it,
you can see that any point on the y-axis will have an x-value of zero. So to get the y-value
from this equation, you can set x equal to zero and solve for y. When you do set the value
of x equal to zero, the equation reduces to:
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{{{5*0 - 8y = 16}}}
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and the 5*0 term is equal to zero so it drops out and the equation is down to:
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{{{-8y = 16}}}
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Now you can solve for y by dividing both sides of the equation by -8 to get:
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{{{y = 16/(-8) = -2}}}
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We now know that the graph crosses the y-axis at the point (0, -2).
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Again you have to think about the point where the graph crosses the x-axis. Any point on the
x-axis will have a y-value of zero.  Therefore, in the given equation if we set y equal to zero
the value of x that we get identifies the point where the graph crosses the x-axis.
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So set y equal to zero and the equation becomes:
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{{{5x - 8*0 = 16}}}
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The -8*0 term multiplies out to zero and, therefore, drops from the equation, leaving just
the equation:
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{{{5x = 16}}}
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You can now solve for x by dividing both sides by 5 to get:
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{{{x = 16/5}}}
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So the x-intercept point is at (16/5, 0}
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Plot this point along with the previous y-intercept point of (0, -2) and you have two points
that you can use to draw the graph.
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When you get done your graph should look like this:
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{{{graph(300,300,-10,10,-10,10,(-5x+16)/(-8))}}}
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Hope this helps you to see your way through the problem.