Question

Consider the line 9x - 7y = -3.What is the slope of a line parallel to this line?What is the slope of a line perpendicular to this line?

Answer 1

Given:

`9x-7y=-3`

The given equation of the line is written in standard form.

We will write the equation in slope-intercept form, we will solve the equation for (y) as follows:

`\begin{gathered} 9x-7y=-3 \\ -7y=-9x-3\rightarrow(/(-7)) \\ (-7y)/(-7)=(-9x)/(-7)+(-3)/(-7) \\ \\ y=(9)/(7)x+(3)/(7) \end{gathered}`

So, the slope of the line = 9/7

We will answer the following questions:

a) What is the slope of a line parallel to this line?

The parallel lines have the same slope

So, the slope of a parallel line = 9/7

b) What is the slope of a line perpendicular to this line?

the product of the slopes of the perpendicular lines = -1

So, we will find the negative of the reciprocal of the given slope

So, the slope of the perpendicular line = -7/9