Question

Consider the line 2x - 7y = - 5 What is the slope of a line parallel to this line? What is the slope of a line perpendicular to this line?

Answer 1

To find the slope of a line from its equation, you have to put the equation in the form

`y=mx+b`

Where m is the slope

Since the given equation is

`2x-7y=-5`

Add 7y to both sides

`\begin{gathered} 2x-7y+7y=-5+7y \\ 2x=-5+7y \end{gathered}`

Add 5 to both sides

`\begin{gathered} 2x+5=-5+5+7y \\ 2x+5=7y \end{gathered}`

Switch the 2 sides

`7y=2x+5`

Divide all terms on both sides by 7

`\begin{gathered} (7y)/(7)=(2x)/(7)+(5)/(7) \\ \\ y=(2)/(7)x+(5)/(7) \end{gathered}`

The slope of the given line is

`m=(2)/(7)`

Since parallel lines have the same slopes, then

The slope of the parallel line is 2/7

Since the product of the slopes of the perpendicular lines is -1, then

To find the slope of the perpendicular line reciprocal of the value and change the sine

Then the slope of the perpendicular line is

`m_P=-(7)/(2)`

The slope of the perpendicular line is -7/2