Chapter 3.4, Problem 61STP

To determine

To find which equation describe the line that passes through the point at $(-2,1)$ and is perpendicular to the line $y=\frac{1}{3}x+5$ .

Answer to Problem 61STP

Option (H) is answer.

Explanation of Solution

Given information:

Line passes through $(-2,1)$

Line perpendicular to $y=\frac{1}{3}x+5$

Formula used:

For perpendicular lines

  $m_1\times m_2=-1$

Calculation:

Let required line is $y=m_{1}x+c$

Here

  $m_1$ is slope of required line

  $c$ is y-intercept of required line

Given line

  $y=\frac{1}{3}x+5$

  $m_2=\frac{1}{3}$

When lines are perpendicular

Then

  $m_1\times m_2=-1$

Then slope of required line is

  $m_1\times \frac{1}{3}=-1$

On solving

  $m_1=-3$

From four options slope $m_1=-3$ having option (H)

Checking point $(-2,1)$ passes through equation of opton (H)

  $1=-3\times -2-5$

On solving

  $1=6-5$

On solving

  $1=1$

True

Hence, option (H) is answer.