Question

Write an equation of the line passing through point P(0, 0) that is perpendicular to the line y = −9x−1 .

Answer 1

A line perpendicular to another line has to have the negative reciprocal of the other's slope, so any equation with the slope 1/9 is perpendicular to that line.

Answer 2

an equation of the line passing through point P(0, 0) that is perpendicular to the given line is

$y=\frac{1}{9} x$

Given :

the line passing through point P(0, 0) that is perpendicular to the line

y = −9x−1

The given equation is in the form of y=mx+b

where m is the slope and b is the y intercept

Find out slope from the given equation y=-9x-1

Slope of the given equation is -9

Slope of perpendicular lines are negative reciprocal of one another

slope of perpendicular line is negative reciprocal of -9 is $\frac{1}{9}$

slope of perpendicular line m=$\frac{1}{9}$

The line passes through the point (0,0) that means y intercept is 0

the value of b=0

$m=\frac{1}{9} , b=0\\y=mx+b\\y=\frac{1}{9} x+b\\y=\frac{1}{9} x$

an equation of the line passing through point P(0, 0) that is perpendicular to the line y = −9x−1 is

$y=\frac{1}{9} x$

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