Question

Find an equation for the line with the given properties. Perpendicular to the line x - 6y = 8; containing the point (4,4) O 1) y = 6x - 28 2) y = - (1/6) > - (14/3) 3) y = - 6x + 28 4) y = - 6x - 28

Answer 1

Answer:

Option 3 - $y=-6x+28$

Step-by-step explanation:

Given : Perpendicular to the line $x - 6y = 8$; containing the point (4,4).

To Find : An equation for the line with the given properties ?

Solution :

We know that,

When two lines are perpendicular then slope of one equation is negative reciprocal of another equation.

Slope of the equation $x - 6y = 8$

Converting into slope form $y=mx+c$,

Where m is the slope.

$y=\frac{x-8}{6}$

$y=\frac{x}{6}-\frac{8}{6}$

The slope of the equation is $m=\frac{1}{6}$

The slope of the perpendicular equation is $m_1=-\frac{1}{m}$

The required slope is $m_1=-\frac{1}{\frac{1}{6}}$

$m_1=-6$

The required equation is $y=-6x+c$

Substitute point (x,y)=(4,4)

$4=-6(4)+c$

$4=-24+c$

$c=28$

Substitute back in equation,

$y=-6x+28$

Therefore, The required equation for the line is $y=-6x+28$

So, Option 3 is correct.