Once you know the slope of the given line, remember that the slope of a perpendicular line is the negative reciprocal (flip the fraction and change the sign).

Line $p$ must pass through $(5,-4)$, so use point-slope form with the perpendicular slope and this point to write an equation.

Rewrite your equation into the form $Ax + By = C$ (no fractions) and see which option has the same coefficients and constant term.

In an expression line, type (-1 - 3) / (4 - (-2)) to compute the slope of the line through $(-2,3)$ and $(4,-1)$. Note the value shown (it should be a negative fraction).

Take the negative reciprocal of the value from step 1 (flip the fraction and change the sign). For example, if Desmos shows $-2/3$, then the perpendicular slope is $3/2$.

In separate expression lines, type each option exactly as written: 2x + 3y = 23, 3x - 2y = 23, 2x + 3y = -23, and 3x + 2y = 23. Desmos will graph all four lines.

Check which graphed line has the perpendicular slope from step 2 and passes through the point $(5,-4)$ (you can click on the graph near $(5,-4)$ to see whether the point lies on that line). The line that meets both conditions is the correct choice.

Use the slope formula with the points $(-2,3)$ and $(4,-1)$:

So, the slope of the line through $(-2,3)$ and $(4,-1)$ is $-\tfrac{2}{3}$.

Perpendicular lines have slopes that are negative reciprocals of each other.

• The slope of the given line is $-\tfrac{2}{3}$.
• Flip the fraction and change the sign to get the perpendicular slope:

Line $p$ passes through $(5,-4)$ and has slope $\tfrac{3}{2}$.

Use point-slope form, $y - y_1 = m(x - x_1)$, with $(x_1,y_1) = (5,-4)$ and $m = \tfrac{3}{2}$:

Now solve for $y$ to get slope-intercept form:

Start from the slope-intercept form you found and convert it to the standard form used in the answer choices:

So, an equation of line $p$ is $3x - 2y = 23$, which corresponds to choice B.