document.write( "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 \n" ); document.write( "
Algebra.Com's Answer #84101 by bucky(2189)\"\" \"About 
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If two lines are parallel they will have the same slope. So first you need to find the slope
\n" ); document.write( "of the given line 2y - 16x = 3.
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\n" ); document.write( "To find the slope you can work this equation into the slope intercept form of y = mx + b.
\n" ); document.write( "When you get it into this form you will know that the slope is m ... the constant that multiplies
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\n" ); document.write( "Start with:
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\n" ); document.write( "2y - 16x = +3
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\n" ); document.write( "get rid of the -16x on the left side by adding 16x to both sides to get:
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\n" ); document.write( "2y = +16x + 3
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\n" ); document.write( "Solve for y by dividing all terms on both sides by 2 ... the multiplier of y. When you do
\n" ); document.write( "this division you get:
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\n" ); document.write( "y = (16/2)*x + 3/2
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\n" ); document.write( "In the first term on the right side the division 16/2 = 8. So the equation becomes:
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\n" ); document.write( "y = 8x + 3/2
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\n" ); document.write( "Note that this is now in the slope intercept form of y = mx + b. Therefore, the multiplier
\n" ); document.write( "of the x term is the slope. So the slope is +8. Any line that is parallel to this line
\n" ); document.write( "must have a slope of 8.
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\n" ); document.write( "So far we know that the slope of a parallel line must be of the form:
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\n" ); document.write( "y = 8x + b
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\n" ); document.write( "Next the problem tells us that the parallel line we are looking for goes through the point (8, 2).
\n" ); document.write( "That means that when x = 8 and y = 2, the equation must be true. So we can take our form:
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\n" ); document.write( "y = 8x + b
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\n" ); document.write( "and substitute 8 for x and 2 for y and then find the value of b. Making these two substitutions
\n" ); document.write( "for x and y, we transform the equation to:
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\n" ); document.write( "2 = 8*8 + b
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\n" ); document.write( "The 8*8 multiplies out to 64 which makes the equation:
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\n" ); document.write( "2 = 64 + b
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\n" ); document.write( "Get rid of the 64 on the right side by subtracting 64 from both sides and the equation
\n" ); document.write( "becomes:
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\n" ); document.write( "-62 = b
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\n" ); document.write( "So in our equation for the parallel line we are trying to find, we can substitute
\n" ); document.write( "-62 for b and the equation becomes:
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\n" ); document.write( "y = 8x - 62
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\n" ); document.write( "This is the equation of a line that is parallel to the given line and goes through the
\n" ); document.write( "point (8, 2). Let's graph the two lines and see what they look like. In the following graph
\n" ); document.write( "the red line is the graph of the equation 2y - 16x = 3 and the green line is the graph of the
\n" ); document.write( "line we found that is parallel to the red line and also goes through the point (8, 2) ....
\n" ); document.write( "the graph of y = 8x - 62
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\n" ); document.write( "\"graph%28+800%2C800%2C+-20%2C20%2C-80%2C80%2C8x%2B1.5%2C8x-62%29\"
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\n" ); document.write( "Hope this helps you to understand the problem and how to do it.
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