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

Since lines are perpendicular and intersect at the origin. Therefore point of intersection would be (0, 0)
since slope of first line i.e. m1 = 3
therefore slope of second line will be \[m_2= \frac{-1}{m_1}= \frac{-1}{3}\]
Equation of required line in slope point form is given as:
\[y-y_1=m_2(x-x_1) \] where x1=0 and y1= 0
\[\rightarrow y-0=\frac{-1}{3}(x-0) \rightarrow \]
\[\rightarrow y=\frac{-1}{3}x\]
\[\rightarrow y=\frac{-x}{3}\]
\[3y=-x \rightarrow x+3y = 0\] is the required eq of the line

Answer 2

@laceyrosexo