The slope of a line that is perpendicular to a line whose equation is −2y = 3x + 7 is [tex]\frac{2}{3}[/tex]
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:
[tex]-2y = 3x + 7\\\\-y = \frac{3}{2}x + \frac{7}{2}\\\\y = \frac{-3}{2}x - \frac{7}{2}[/tex]
On comparing the above equation with slope intercept form,
[tex]m = \frac{-3}{2}[/tex]
We know that product of slope of a line and slope of line perpendicular to it is -1
Therefore,
[tex]\frac{-3}{2} \times \text{ slope of line perpendicular to it } = -1\\\\ \text{ slope of line perpendicular to it } = \frac{2}{3}[/tex]
Thus slope of line that is perpendicular to given line is [tex]\frac{2}{3}[/tex]
