Question

What is the equation of the line that is perpendicular to the line y equal minus 1 over 2 open parentheses x minus 18 close parentheses and intersects the y-axis at open parentheses 0 comma space minus 1 close parentheses ?

Answer 1

Given:

The equation of line is

$y=-\dfrac{1}{2}(x-18)$

The perpendicular line intersect the y-axis at (0,-1).

To find:

Equation of perpendicular line.

Solution:

Point slope form of a line is $y-y_1=m(x-x_1)$, where m is slope.

We have,

$y=-\dfrac{1}{2}(x-18)$

Thus, the slope of this line is $m_1=-\dfrac{1}{2}$.

Product of slopes of two perpendicular lines is -1.

Let the slope of perpendicular line is $m_2$. Then,

$m_1\times m_2=-1$

$-\dfrac{1}{2}\times m_2=-1$

$m_2=2$

Slope of perpendicular line is 2 and it passes through (0,-1). So, the equation of perpendicular line is

$y-(-1)=2(x-0)$

$y+1=2x$

$y=2x-1$

Therefore, equation of perpendicular line is $y=2x-1$.