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Question

In the following figure, the line passes through the origin and through P=(1,3). Find the equation of a line which passes through P and is perpendicular to the first.
484573_0dc406ce53d74a0b805639f262f631e4.png

A
y=3x+4
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B
y=13x+4
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C
y=13x+103
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D
y=13x+4
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E
y=13x+103
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Solution

The correct option is E y=13x+103
The line shown in the above figure passes through (0,0) and (1,3).
So the slope of the line m=y2y1x2x1=3010=31=3
Thus the line which passes through P(1,3) and perpendicular to the first have a negative reciprocal slope which is 13.
So, the equation of the line is
y=mx+b
3=13(1)+b
3=13+b
b=3+13
b=103
Put the value to find the equation
y=13x+103

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