Chapter 3.4, Problem 52PPS

To determine

To write in point-slope form for the line parallel to $y+11=\frac{1}{2}(4x+6)$ and contain

  $(5,3)$

Answer to Problem 52PPS

Slope intercept form

  $y=2x-7$

Explanation of Solution

Given information:

Line parallel to $y+11=\frac{1}{2}(4x+6)$ and contain $(5,3)$

Formula used:

Point-slope form

  $y-y_1=m(x-x_1)$

Calculation:

Given line

  $y+11=\frac{1}{2}(4x+6)$

On solving

  $y+11=2x+3$

Subtract 11 both sides

  $y+11-11=2x+3-11$

On solving

  $y=2x-8$

Then slope of given line

  $m_2=2$

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

Here

  $m_1$ is slope of required line

  $b$ is y-intercept of required line

When lines are parallel

Then

  $m_1=m_2$

Then slope of required line is

  $m_1=2$

Then slope and point containing by required line

  $m_1=2$

  $(5,3)$

Here

  $x_1=5$

  $y_1=3$

Using point slope formula

  $y-3=2(x-5)$

On solving

  $y-3=2x-10$

Add 3 both sides

  $y-3+3=2x-10+3$

On solving

  $y=2x-7$

Hence, slope intercept form is $y=2x-7$