Question

Consider the line 7x+5y=−2.

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

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

Answer 1

Answer: slope of a line perpendicular is
`(5)/(7)`; slope of a line parallel to this line is
`-(7)/(5)`.

Explanation:

Rewrite the line in y = mx + b form, where m is slope and b is y-intercept.

7x + 5y = -2

5y = -7x -2

y =
`-(7)/(5)`x -
`(2)/(5)`

The product of two slope of perpendicular line is -1.

Let x be the other line that perpendicular line with the line 7x + 5y = -2.

（
`-(7)/(5)`)x = -1

x =
`(5)/(7)`

The slope of a line parallel to this line is the same, which is
`-(7)/(5)`.