Question

find the equation of a line that is perpendicular to Y =1/ 4x + 6 and contains the point (-2,0)

Answer 1

Answer:

The equation of perpendicular line is $y=-4x-8$.

Step-by-step explanation:

The equation of given line is

$y=\frac{1}{4}x+6$             ..... (1)

The slope intercept form of a line is

$y=mx+b$                         .... (2)

Where, m is slope and the y-intercept is b.

On comparing (1) and (2) we get the slope of line is $\frac{1}{4}$ and the y-intercept is 6.

The product of slopes of two perpendicular line is -1.

$m_1\times m_2=-1$

$\frac{1}{4}\times m_2=-1$

$m_2=-4$

The slope of perpendicular line is -4. It is given that the perpendicular line passing through the point (-2,0).

Using point slope form we get

$y-y_1=m(x-x_1)$

$y-0=-4(x-(-2))$

$y=-4x-8$

Therefore the equation of perpendicular line is $y=-4x-8$.