You can put this solution on YOUR website! the slope parallel to -4 is the same as -4 which equals -4
the slope perpendicular to -4 is the negative reciprocal of - 4 = 1/4
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if the slope were 5/3, then parallel would be 5/3 and perpendicular would be -3/5.
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if the slope were -9/5 then parallel would be -9/5 and perpendicular would be 5/9
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the reciprocal of any number is that number divided into 1.
example:
reciprocal of 5 = 1/5
reciprocal of 3/5 = 1 divided by 3/5 which is the same as 1 * 5/3 = 5/3
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in your example, the original slope is -4.
one equation of that line would be y = -4x + 2
equation of a line perpendicular to that would be y = (1/4)*x + 2
graph will look like this:
the line with the slope of -4 is going up from right to left.
the line with slope 1/4 is going up from left to right.
they intersect at the point (0,2) and are perpendicular to each other because the slopes are negative reciprocals of each other.
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a line parallel to the line y = (1/4)*x + 2 but 5 units below it would be given by the equation y = (1/4)*x - 3
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a graph of that equation looks like this:
the top line is y = (1/4)*x + 2
the bottom line is y = (1/4)*x - 3
they are parallel to each other because the slopes are equal to each other.
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