Question

Consider the line 4x+9y=9.

What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?
Slope of a parallel line:
Slope of a perpendicular line:

Answer 1

4x + 9y = 9
9y = -4x + 9
y = -4/9x + 1

The gradient of parallel lines is -4/9
The gradient of perpendicular lines is 9/4 [the negative reciprocal of m]

Answer 2

Parallel:
`-\frac49`

Perpendicular:
`\frac94`

Explanation:

Hello!

First let's find the slope of the line given. Convert it to Slope-Intercept Form.

Slope-Intercept Form:
`y = mx + b`

Convert

• 
  `4x + 9y = 9`
• 
  `9y = -4x + 9`
• 
  `y = -\frac49x+1`

Parallel Lines

Parallel lines have the same slope but a different y-intercept. Therefore, the slope of the parallel line is still
`-\frac49`.

Perpendicular Lines

Perpendicular lines have the opposite reciprocal slope, which means you have to flip the sign (+/-), and the numerator and denominator. The slope of the perpendicular line is
`\frac94`.