SOLUTION: Determine the equation of the line that passes through the point (8,2) and is parallel to the line 2 y - 16 x = 3. Select the correct answer in slope-intercept form
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Question 115513: Determine the equation of the line that passes through the point (8,2) and is parallel to the line 2 y - 16 x = 3. Select the correct answer in slope-intercept form Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website! If two lines are parallel they will have the same slope. So first you need to find the slope
of the given line 2y - 16x = 3.
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To find the slope you can work this equation into the slope intercept form of y = mx + b.
When you get it into this form you will know that the slope is m ... the constant that multiplies
the x.
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Start with:
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2y - 16x = +3
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get rid of the -16x on the left side by adding 16x to both sides to get:
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2y = +16x + 3
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Solve for y by dividing all terms on both sides by 2 ... the multiplier of y. When you do
this division you get:
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y = (16/2)*x + 3/2
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In the first term on the right side the division 16/2 = 8. So the equation becomes:
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y = 8x + 3/2
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Note that this is now in the slope intercept form of y = mx + b. Therefore, the multiplier
of the x term is the slope. So the slope is +8. Any line that is parallel to this line
must have a slope of 8.
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So far we know that the slope of a parallel line must be of the form:
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y = 8x + b
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Next the problem tells us that the parallel line we are looking for goes through the point (8, 2).
That means that when x = 8 and y = 2, the equation must be true. So we can take our form:
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y = 8x + b
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and substitute 8 for x and 2 for y and then find the value of b. Making these two substitutions
for x and y, we transform the equation to:
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2 = 8*8 + b
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The 8*8 multiplies out to 64 which makes the equation:
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2 = 64 + b
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Get rid of the 64 on the right side by subtracting 64 from both sides and the equation
becomes:
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-62 = b
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So in our equation for the parallel line we are trying to find, we can substitute
-62 for b and the equation becomes:
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y = 8x - 62
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This is the equation of a line that is parallel to the given line and goes through the
point (8, 2). Let's graph the two lines and see what they look like. In the following graph
the red line is the graph of the equation 2y - 16x = 3 and the green line is the graph of the
line we found that is parallel to the red line and also goes through the point (8, 2) ....
the graph of y = 8x - 62
.
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Hope this helps you to understand the problem and how to do it.
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