Question

What is the slope of a line perpendicular to the line whose equation is 3x + 2y = 14. Fully simplify your answer.

Answer 1

`\displaystyle(2)/(3)`

Explanation:

Perpendicular lines are lines that meet at a right angle.

Slope of Perpendicular Lines

All perpendicular lines have the same relationship between the slopes. The slope of a perpendicular line will be the opposite reciprocal of the slope of the original line.

This means to find the slope of the line perpendicular to 3x + 2y = 14, we first need to find its slope. One of the easiest ways to do this is to convert the equation into slope-intercept.

Slope-Intercept Form

Slope-intercept form is given by y=mx+b, where m is the slope and b is the y-intercept. To go from standard form to slope-intercept, just solve for y.

• 3x + 2y = 14

First, subtract 3x

• 2y = -3x +14

Then, divide by 2

• 
  `y=-(3)/(2)x+7`

This means that the slope of the given line is -3/2. Now we can take the opposite reciprocal. By flipping the fraction and changing the sign we get the slope 2/3. Thus, the slope of a line perpendicular to the given equation is 2/3.