Chapter 3.4, Problem 55HP

To determine

To find the value of n so that the line perpendicular to the line with the equation $-2y+4=6x+8$ passes through the point at $(n,-4)$ and $(2,-8)$ .

Answer to Problem 55HP

  $n=14$

Explanation of Solution

Given information:

Line perpendicular to $-2y+4=6x+8$

Line passes through the points at $(n,-4)$ and $(2,-8)$ .

Formula used:

Slope, $m=\frac{y_2-y_1}{x_2-x_1}$

Calculation:

Line passes through the points at $(n,-4)$ and $(2,-8)$ .

Here

  $x_1=n$

  $y_1=-4$

  $x_2=2$

  $y_2=-8$

Using slope formula to calculate slope of line

  $m=\frac{-8-(-4)}{2-n}$

On solving

  $m=\frac{-4}{2-n}$

Given line

  $-2y+4=6x+8$

Subtract 4 both side

  $-2y+4-4=6x+8-4$

On solving

  $-2y=6x+4$

Divide by 2 both side

  $\frac{-2y}{2}=\frac{6x+4}{2}$

On solving

  $-y=3x+2$

On simplify

  $y=-3x-2$

Then slope of given line is

  $m_2=-3$

When lines are perpendicular

Then

  $m_1\times m_2=-1$

Substitute value of slopes of perpendicular lines

Then

  $\frac{-4}{2-n}\times -3=-1$

On solving

  $12=n-2$

Add 2 both side

  $12+2=n-2+2$

Then

  $n=14$

Hence, answer is $n=14$