Question

A line passes through (-3, -2) and is perpendicular to 3x - 2y = 7.

Answer 1

When graphing this, the answer that I derived was y = -2/3x -4

Answer 2

Answer: $y=\dfrac{-2}{3}x-4$

Step-by-step explanation:

The given equation of  line :

$3x-2y=7\\\\\Rightarrow\ y=\dfrac{3}{2}x-\dfrac{7}{2}$, comparing to  the standard equation of line $y=mx+c$, the slope of line =$m= \dfrac{3}{2}$

Also, when two lines are perpendicular , then the product of their slope is -1.

Therefore, the slope of line perpendicular to the given line =$\dfrac{-1}{\dfrac{3}{2}}=\dfrac{-2}{3}$

Now, the equation of the line passing from (-3, -2) with slope $\dfrac{-2}{3}$ is given by ;-

$(y-(-2))=\dfrac{-2}{3}(x-(-3))\\\\\Rightarrow\ y=\dfrac{-2}{3}(x+3)-2\\\\\Rightarrow\ y=\dfrac{-2}{3}x-4$

Hence, the equation of the line in slope-intercept form L

$y=\dfrac{-2}{3}x-4$