Chapter 3.3, Problem 58STP

To determine

To find the graph of which equation passes through $(-3,-2)$ and is perpendicular to the graph of $y=\frac{3}{4}x+8$ .

Answer to Problem 58STP

Option (A) is answer.

Explanation of Solution

Given information:

Line passes through $(-3,-2)$

Line perpendicular to $y=\frac{3}{4}x+8$

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

  $y=\frac{3}{4}x+8$

  $m_2=\frac{3}{4}$

When lines are perpendicular

Then

  $m_1\times m_2=-1$

Then slope of required line is

  $m_1\times \frac{3}{4}=-1$

On solving

  $m_1=-\frac{4}{3}$

From four options slope $m_1=-\frac{4}{3}$ having option (A) and option (B)

Checking point $(-3,-2)$ passes through equation of opton (A)

  $-2=-\frac{4}{3}(-3)-6$

On solving

  $-2=4-6$

On solving

  $-2=-2$

True

Hence, option (A) is answer.