Question

What is the slope of a line perpendicular to the line whose equation is

2x + 3y = -3. Fully simplify your answer.

Answer 1

`(3)/(2)`

Explanation:

To find the slope of the perpendicular line, we must first find the slope of the given line.

This can be done by rearranging the equation into the slope intercept form.

2x +3y= -3

3y= -2x -3

y= -⅔x -1

Thus, the slope of the given line is -⅔.

The slope of the perpendicular line is the negative reciprocal of the given line.

Slope of perpendicular line
`= (3)/(2)`

What is slope-intercept form?

• y= mx +c, where m is the slope and c is the y-intercept
• This can be achieved by making y the subject of formula

Negative reciprocal

• The reciprocal of m is
  `(1)/(m)`
• The negative reciprocal of m is
  `- (1)/(m)`

Negative reciprocal of -⅔

`= - 1 / ( - (2)/(3) )`

`= - 1 * ( - (3)/(2) )`

`= (3)/(2)`