ANSWER
The two lines are perpendicular if [tex]m_1 \times m_2 = - 1[/tex]
EXPLANATION
Given two lines:
[tex]y=m_1x+b_1[/tex]
and
[tex]y=m_2x+b_2[/tex]
We can tell wether these two lines are perpendicular to each other using their slopes.
If the product of their slopes is -1, the then the two line are perpendicular.
For example:
The line
[tex]y = 2x + 6[/tex]
has slope
[tex]m_1= 2[/tex]
and the line
[tex]y = - \frac{1}{2} x + 1[/tex]
has slope
[tex]m_2 = - \frac{1}{2} [/tex]
The product of the two slopes is
[tex]m_1 \times m_2 = 2 \times - \frac{1}{2} [/tex]
This implies that:
[tex]m_1 \times m_2 = - 1[/tex]
Therefore the two lines are perpendicular.
