The line y = 7x + 2 perpendicular to the [tex]y=-\frac{1}{7} x+12[/tex].
Solution:
Equation of one line:
[tex]y=7 x+2[/tex]
Slope of this line:
[tex]m_1=7[/tex]
Equation of another line:
[tex]$ y=-\frac{1}{7} x+12[/tex]
Slope of this line:
[tex]$m_2=-\frac{1}{7}[/tex]
If two lines are perpendicular, then the product of their slope is -1.
[tex]$m_1 \times m_2=7 \times\frac{-1}{7}[/tex]
Both 7's get canceled, we get
[tex]$m_1 \times m_2=-1[/tex]
Therefore, product of slopes of the given lines are -1.
Hence, the line y = 7x + 2 perpendicular to the [tex]y=-\frac{1}{7} x+12[/tex].
