Answer: [tex]y=\dfrac{-2}{3}x-4[/tex]
Step-by-step explanation:
The given equation of line :
[tex]3x-2y=7\\\\\Rightarrow\ y=\dfrac{3}{2}x-\dfrac{7}{2}[/tex], comparing to the standard equation of line [tex]y=mx+c[/tex], the slope of line =[tex] m= \dfrac{3}{2}[/tex]
Also, when two lines are perpendicular , then the product of their slope is -1.
Therefore, the slope of line perpendicular to the given line =[tex]\dfrac{-1}{\dfrac{3}{2}}=\dfrac{-2}{3}[/tex]
Now, the equation of the line passing from (-3, -2) with slope [tex] \dfrac{-2}{3}[/tex] is given by ;-
[tex](y-(-2))=\dfrac{-2}{3}(x-(-3))\\\\\Rightarrow\ y=\dfrac{-2}{3}(x+3)-2\\\\\Rightarrow\ y=\dfrac{-2}{3}x-4[/tex]
Hence, the equation of the line in slope-intercept form L
[tex]y=\dfrac{-2}{3}x-4[/tex]
