Question

What is the slope of a line that is perpendicular to a line whose equation is −2y=3x+7 ?

Answer 1

The slope of a line that is perpendicular to a line whose equation is −2y = 3x + 7 is $\frac{2}{3}$

Solution:

Given that we have to find the slope of the line that is perpendicular to a line whose equation is −2y = 3x + 7

The slope intercept form is given as:

y = mx + c

Where "m" is the slope of line and "c" is the y - intercept

Given equation is:

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

On comparing the above equation with slope intercept form,

$m = \frac{-3}{2}$

We know that product of slope of a line and slope of line perpendicular to it is -1

Therefore,

$\frac{-3}{2} \times \text{ slope of line perpendicular to it } = -1\\\\ \text{ slope of line perpendicular to it } = \frac{2}{3}$

Thus slope of line that is perpendicular to given line is $\frac{2}{3}$