Chapter 3.4, Problem 50PPS

To determine

To write in point-slope form for the line parallel to $y-2=3(x+7)$ and contain

  $(4,2)$

Answer to Problem 50PPS

Slope intercept form

  $y=3x-10$

Explanation of Solution

Given information:

Line parallel to $y-2=3(x+7)$ and contain $(4,2)$

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

  $y-2=3(x+7)$

On solving

  $y-2=3x+21$

Add 2 both sides

  $y-2+2=3x+21+2$

On solving

  $y=3x+23$

Then slope of given line

  $m_2=3$

When lines are parallel

Then

  $m_1=m_2$

Then slope of required line is

  $m_1=3$

Then slope and point containing by required line

  $m_1=3$

  $(4,2)$

Here

  $x_1=4$

  $y_1=2$

Using point slope formula

  $y-2=3(x-4)$

On solving

  $y-2=3x-12$

Add 2 both sides

  $y-2+2=3x-12+2$

On solving

  $y=3x-10$

Hence, slope intercept form is $y=3x-10$