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Question 83574: can you please help me solve these 2 and graph the lines-- it must be put in slope intercept form so I can identify the slope and y thank you
x + 2y = 6 I'm not sure is it (1/2,3)
2x + y = 9 I'm not sure is it (2,6)
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! First Problem. Given:
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To get this into slope intercept form, you need to solve for y. This means that you need
to get the y-term by itself on one side of the equation. So you need to start by getting
rid of the x term on the left side of the given equation. You can do this by subtracting
x from the left side, but if you do then you must also subtract x from the right side too
to keep the equation in balance. So subtract x from the left AND right sides to get:
.
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But you are trying to solve for y and you have 2y on the left side. So divide the left
side by the multiplier of y (which is 2). However, if you divide the left side by 2, then
you must also divide both terms on the right side by 2. Dividing both sides by 2 results in:
.
.
This is the slope intercept form of the given equation. You can tell from this form that
the slope is  and the graph crosses the y-axis at a value of +3.
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You seem to have had the correct idea, but made an error in the sign of the slope.
The minus sign means that the graph goes down as you move to the right on the graph, and
your answer of + would have the graph moving upward as you move to the right on
the graph. The graph below shows the correct graph:
.
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You can quickly check the graph by returning to the original equation for this first
problem:
.
.
Set x equal to zero and this equation becomes  . Then divide both sides by 2 and the
equation reduces to  . This tells you that the (x,y) point (0,3) should be
on the graph. Next set y equal to zero and the equation reduces to  . This
tells you that the (x,y) point (6,0) should also be on the graph. I think you'll find
that (0,3) and (6,0) are both on the graph ... which helps to verify that the graph is
correct.
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Second Problem. Given
.
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The same general process as we used in the first problem applies here. Solve for +y
by subtracting 2x from both sides of the given equation. This subtraction leads to:
.
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This is in slope-intercept form. The slope is -2 and the intercept is +9. The graph is:
.
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You can again check the graph by returning to the original equation for this second
problem. This equation was:
.
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Set x equal to zero in the equation and the equation becomes  . So one (x,y) point on
the graph should be (0,9). Then set y equal to 0 and the equation becomes  .
When you then divide both sides by 2 you get  . So the (x,y) point (4.5, 0)
should be on the graph too.
.
It appears as if you have the correct idea, but just made the same sign error in getting
the equations for the two problems into the slope-intercept form. Notice that since both
of these problems resulted in a negative slope, the two graphs go down as you move to
the right along the graph.
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Hope this helps you to understand the process a little better and that the discussion
helps you too.
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