Question 81947
Given:
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the lines y - 4x = -1 and x + 4y =12
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find whether the lines are parallel, perpendicular, or neither.
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To do this problem you need to know the slope of each line.  If the slopes are identical
the lines are either parallel or co-linear (one on top of the other). If the slopes are
negative inverses, the lines are perpendicular. Examples of negative inverses are:
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6 and -1/6
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-3 and +1/3
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A way you can find the slope is to convert the equation for each line to the slope-intercept
form of:
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y = mx + b
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If you get the equation of the line in this form, m, which is the multiplier of the x term,
is the slope and b is the point on the y-axis where the line intersects.
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Let's rearrange the equation of the first line into the slope-intercept form.
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y - 4x = -1
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Get rid of the -4x on the left side by adding 4x to both sides.  When you add 4x to both 
sides the equation becomes:
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y = 4x -1
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Note that this is in the slope intercept form. The slope of this line is +4 (which is the
multiplier of the x) and the line crosses the y-axis at -1.
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Let's now work the second equation into the slope intercept form.
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x + 4y = 12
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get rid of the x on the left side by subtracting x from both sides.  This
subtraction changes 
the equation to:
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4y = -x + 12
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Divide both sides by 4 to solve for y:
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y = -x/4 + 12/4 
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and this simplifies to:
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y = (-1/4)x + 3
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In this equation the slope is -1/4 and the line crosses the y-axis at +3.
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Compare the two slopes. One line has a slope of +4 and the other a slope of -1/4. 
The slopes are negative inverses and, therefore, the two lines are perpendicular.
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Cheers!!!