Question

What is the slope of a line perpendicular to 3x+2y = 7?​

Answer 1

Answer:

2/3

Step-by-step explanation:

First find the slope of the line

3x+2y = 7

Subtract 3x

2y = -3x+7

Divide by 2

y = -3/2x +7/2

This is in slope intercept form  y = mx+b  where m is the slope

The slope is -3/2

A line perpendicular is the negative reciprocal

-1/(-3/2)

2/3

The slope of the perpendicular line is 2/3

Answer 2

Answer:

Slope of the line perpendicular to the given line = 2/3

Step-by-step explanation:

The product of the slopes of lines perpendicular to each other is - 1

That is,

      $slope_{1} \times slope _ 2 = - 1$

Given equation of the line :

                                  3x + 2y = 7

                                          2y = - 3x + 7

                                          $y = -\frac{3}{2}x + \frac{7}{2}$

$Therefore, \ slope \ of \ the \ given \ line \ , slope _1 = \ -\frac{3}{2}$

Find slope of the line perpendicular to the given line:

$\frac{-3}{2} \times slope_2 = - 1\\\\slope_2 = - 1 \times \frac{2}{-3} = \frac{2}{3}$