Question

Two perpendicular lines intersect at the origin. If the slope of the first line is 3, what is the equation of the second line?. .

Answer 1

The equation of a line is y=mx + b where x is the coordinate in the x-axis, y is the coordinate in the y-axis, m is the slope of the line and b is the y-intercept.

For perpendicular lines, the slope of the second line is the negative reciprocal of the first line,
first line: m
second line: -1/m

For this case, if the slope is 3 then the negative slope is -1/3.
If both lines intersect at the origin then b=0

The equation of the second line is then, y=-1/3x

Answer 2

The general equation of a line is expressed as:

y = mx + b where m is the slope of the line and b is the y-intercept.

If the lines in this problem intersect at the origin, then the equation reduce to:

y = mx

For the first line, it was stated that the slope is 3 then the equation for the first line is y = 3x. If the second line is perpendicular with the first line, then the slope will be the negative of the slope of the first line. Therefore , the equation for the second line is y= -3x.