Chapter 3.4, Problem 37PPS

To determine

To write in point-slope form for the line perpendicular to $y=\frac{1}{2}x+9$ and contain $(-7,-4)$

Answer to Problem 37PPS

Slope intercept form

  $y=-2x-18$

Explanation of Solution

Given information:

Line perpendicular to $y=\frac{1}{2}x+9$ and contain $(-7,-4)$

Formula used:

Point-slope form

  $y-y_1=m(x-x_1)$

Calculation:

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

Here

  $m_1$ is slope of required line

  $b$ is y-intercept of required line

Given line

  $y=\frac{1}{2}x+9$

  $m_2=\frac{1}{2}$

When lines are perpendicular

Then

  $m_1\times m_2=-1$

Then slope of required line is

  $m_1\times \frac{1}{2}=-1$

On solving

  $m_1=-2$

Point containing $(-7,-4)$

  $x_1=-7$

  $y_1=-4$

Using point slope formula

  $y-(-4)=-2(x-(-7))$

On solving

  $y+4=-2(x+7)$

On solving

  $y+4=-2x-14$

Subtract 4 both sides

  $y+4-4=-2x-14-4$

On solving

  $y=-2x-18$

Hence, slope intercept form is $y=-2x-18$