document.write( "Question 73718: A line perpendicular to the line 4x-3y=7. It also has the same y-intercept as the line 5x-4y=20. What is the equation of the line? \n" ); document.write( "
Algebra.Com's Answer #52746 by bucky(2189)\"\" \"About 
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First let's find the slope of the graph of this equation:
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\n" ); document.write( "4x - 3y = 7
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\n" ); document.write( "Convert this line to the slope intercept form. We need to find its slope and the slope intercept
\n" ); document.write( "form makes this easy. The slope intercept form is of the form y = m*x + b where m, the
\n" ); document.write( "multiplier of the x term is the slope. So let's rearrange the given equation into this form.
\n" ); document.write( "Begin with the equation:
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\n" ); document.write( "4x - 3y = 7
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\n" ); document.write( "Eliminate the 4x on the left side by subtracting 4x from both sides to get:
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\n" ); document.write( "-3y = -4x + 7
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\n" ); document.write( "Now multiply both sides of this equation by -1 to get +3y on the left side:
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\n" ); document.write( "3y = 4x - 7
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\n" ); document.write( "Now solve for y by dividing both sides of this equation by 3. The result is:
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\n" ); document.write( "y = (4/3)x -(7/3)
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\n" ); document.write( "This is in the slope intercept form. The slope is the multiplier of the x. It is the
\n" ); document.write( "fraction (4/3). A line that is perpendicular to this line will have the negative inverse
\n" ); document.write( "of 4/3 as its slope. What is meant by negative inverse? First invert the fraction
\n" ); document.write( "so that 4/3 becomes 3/4. Then put a negative sign on it. So the slope of the perpendicular
\n" ); document.write( "line is -(3/4).
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\n" ); document.write( "So far so good. In slope intercept form the perpendicular line will be:
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\n" ); document.write( "y = -(3/4)x + b
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\n" ); document.write( "b is the value on the y-axis where the graph of this perpendicular line crosses the y-axis.
\n" ); document.write( "The problem says this intercept will be the same point as the line 5x - 4y = 20. So what we need
\n" ); document.write( "to do is find the value of y in this equation when x = 0. Think about it. Any point having
\n" ); document.write( "an x value of zero will be on the y-axis. So set x equal to zero and you get:
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\n" ); document.write( "5*0 - 4y = 20 which simplifies to:
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\n" ); document.write( "-4y = 20
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\n" ); document.write( "Find the value of the y intercept by dividing both sides by -4 to get y = -5. Now all
\n" ); document.write( "we have to do is return to our equation for the perpendicular line and put -5 in for b.
\n" ); document.write( "The equation is:
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\n" ); document.write( "y = (-3/4)*x + b and with the substitution this becomes:
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\n" ); document.write( "y = (-3/4)*x - 5
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\n" ); document.write( "That's it ... a line perpendicular to the line 4x - 3y = 7 and having the same y-intercept
\n" ); document.write( "as the line 5x - 4y = 20
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\n" ); document.write( "Hope this helps you to understand perpendicular line generation. \n" ); document.write( "
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