For two lines to be perpendicular, their slopes must be negative reciprocals. If the slope of one line is $\tfrac{3}{2}$, what should the other line's slope be?

Once you know the slope of line $m$ and that it goes through $(-2,3)$, plug these into point-slope form $y - y_1 = m(x - x_1)$ and then rewrite in slope–intercept form.

In Desmos, enter the rearranged form of the given line: type y = (3/2)x - 2 in one expression line to see its graph and note its slope $\tfrac{3}{2}$.

Remember that a perpendicular line must have slope equal to the negative reciprocal of $\tfrac{3}{2}$. Use this value (call it $m$) for the slope of line $m$.

In a new expression line, type y = m*x + b using your perpendicular slope value for m, and make b a slider (Desmos will prompt you). This shows all lines with the correct perpendicular slope as you move the slider.

Plot the point (-2, 3) in Desmos. Adjust the slider for $b$ until the line passes exactly through this point; then read off the resulting equation and match it to the correct answer choice.

The given line is

Solve for $y$ to put it in slope–intercept form.

First, isolate the $y$ term:

Now divide everything by $-4$:

So the slope of the given line is $\tfrac{3}{2}$.

If two lines are perpendicular, the product of their slopes is $-1$. That means the perpendicular slope is the negative reciprocal of the original slope.

The original slope is $\tfrac{3}{2}$, so the perpendicular slope is

So line $m$ must have slope $-\tfrac{2}{3}$.

Line $m$ passes through $(-2,3)$ and has slope $-\tfrac{2}{3}$. Use point-slope form:

Here, $m = -\tfrac{2}{3}$ and $(x_1,y_1) = (-2,3)$, so

Now expand the right side:

Add $3$ to both sides to solve for $y$:

Write $3$ as $\tfrac{9}{3}$ and combine like terms:

This matches choice D, so the equation of line $m$ is $y = -\dfrac{2}{3}x + \dfrac{5}{3}$.