Question

Is the line y=7x+2 perpendicular to the y=-1/7x+12 explain.

Answer 1

The line y = 7x + 2 perpendicular to the $y=-\frac{1}{7} x+12$.

Solution:

Equation of one line:

$y=7 x+2$

Slope of this line:

$m_1=7$

Equation of another line:

$y=-\frac{1}{7} x+12$

Slope of this line:

$m_2=-\frac{1}{7}$

If two lines are perpendicular, then the product of their slope is -1.

$m_1 \times m_2=7 \times\frac{-1}{7}$

Both 7's get canceled, we get

$m_1 \times m_2=-1$

Therefore, product of slopes of the given lines are -1.

Hence, the line y = 7x + 2 perpendicular to the $y=-\frac{1}{7} x+12$.