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Question 115553: Will someone please help me solve this problem? It says to write the equation of the line that contains the point(7,-1) and is parallel to the line y=-2x+4. Express in standard form.
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! The slope intercept form of an equation is y = mx + b and in this form m, the multiplier of
the x is the slope, and b is the value on the y-axis where the line crosses the y axis.
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You are given the equation y = -2x + 4. Notice that this is identical in form to the slope
intercept form. By comparing this given equation to the slope intercept form you can see that
m, the multiplier of x, is -2 in the given equation. And since this multiplier is the slope,
we can say that the slope of the given line is -2.
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Any line that is to be parallel to a given line must have the same slope. Therefore, the
line we are looking for must have a slope of -2. That means that in slope intercept form
the line we are trying to get must be of the form:
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y = -2x + b
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The problem tells us that this line must pass through the point (7, -1). This means that
when x is 7 and y is -1, the equation must be true. Therefore, go to the slope intercept form
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y = -2x + b
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and substitute 7 for x and -1 for y to get:
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-1 = -2*7 + b
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On the right side multiply out -2 times 7 to get -14. This makes the equation:
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-1 = -14 + b
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Get rid of the -14 on the right side by adding 14 to both sides. This makes the equation become:
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13 = b
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Now that we know b must be +13, we can return to our partially developed equation for
the parallel line:
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y = -2x + b
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and substitute +13 for b to make the equation:
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y = -2x + 13
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This answer is in slope intercept form and the problem tells you to put it into standard form.
The standard form of an equation is:
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Ax + By = C
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To convert our answer from slope intercept form to standard form all we have to do is get
rid of the -2x on the right side by adding +2x to both sides. When you do that the slope
intercept equation becomes:
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2x + y = 13
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And this is the form you were to find.
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Let's graph the two equations (the given one and the one we found ...) just to make sure they
are parallel and the one we found also goes through the point (7, -1).
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In the graphs below, the red graph is of the equation given in the problem ...y = -2x + 4
and the green graph is of the line we found, namely ... 2x + y = 13.
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Hope this helps you with the problem and shows you how to determine the equations for
parallel lines.
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