Chapter 3.4, Problem 11CYU

To determine

To write in point-slope form for the line parallel to $y=\text{4}x-5$ and contain $(-1,5)$

Answer to Problem 11CYU

Slope intercept form of line

  $y=4x+9$

Explanation of Solution

Given information:

Line perpendicular to $y=\text{4}x-5$ and contain $(-1,5)$

Formula used:

Point-slope form

  $y-y_1=m(x-x_1)$

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

  $y=\text{4}x-5$

  $m_2=4$

When lines are parallel

Then

  $m_1=m_2$

Then slope of required line is

  $m_1=4$

Point containing $(-1,5)$

  $x_1=-1$

  $y_1=5$

Using point slope formula

  $y-5=4(x-(-1))$

On solving

  $y-5=4(x+1)$

On solving

  $y-5=4x+4$

Add 5 both sides

  $y-5+5=4x+4+5$

On solving

  $y=4x+9$

Hence, slope intercept form is $y=4x+9$