Question

Consider the line 7x+9y=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

The slope of a line parallel to this line will be: -7/9

The slope of the perpendicular line will be:

`(-1)/((-7)/(9))=(9)/(7)`

Explanation:

We know the slope-intercept form

`y=mx+b`

Here,

• m is the slope

• b is the y-intercept

Given the equation

`7x+9y=5`

simplifying to write in the lope-intercept form

`y=-(7)/(9)x+(5)/(9)`

Thus, the slope of the line is: -7/9

The slope of a line parallel to the line:

We have already determined that the slope of the line is: -7/9

• We know that the parallel lines have the same slope.

Thus, the slope of a line parallel to this line will be: -7/9

The slope of a line perpendicular to the line:

We have already determined that the slope of the line is: -7/9

As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line.

Thus, the slope of the perpendicular line will be:

`(-1)/((-7)/(9))=(9)/(7)`