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

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

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.