Once you know the slope of line $m$, use the point $(-4, 9)$ in the form $y - y_1 = m(x - x_1)$ to write its equation, then simplify to $y = mx + b$.

Set your equation for line $m$ equal to $y = 3x - 2$ and solve for $x$. Then plug that $x$ value back into one of the equations to find $y$, and finally add the two coordinates to get $p + q$.

Enter the equations of the two lines into Desmos: first type y = (5/2)x + 19 (for line m) and then type y = 3x - 2 on the next line so both graphs appear.

Click or tap on the point where the two lines cross; Desmos will display the coordinates of the intersection as an ordered pair $(p, q)$.

Use a new expression line to add the intersection coordinates (for example, if the point is labeled A, type A.x + A.y) and check that this matches the value of $p + q$ you found algebraically.

The line is given by $2x + 5y = 7$.

Rearrange to slope-intercept form (solve for $y$):

So the slope of this line is $-\frac{2}{5}$.

Slopes of perpendicular lines in the plane are negative reciprocals of each other.

The given line has slope $-\frac{2}{5}$, so the slope of line $m$ is the negative reciprocal:

Use point-slope form with slope $\frac{5}{2}$ and point $(-4, 9)$:

Distribute and simplify:

So line $m$ has equation $y = \frac{5}{2}x + 19$.

At the intersection point $(p, q)$, both equations for $y$ are equal:

Multiply both sides by 2 to clear the fraction:

Subtract $5x$ from both sides:

Add 4 to both sides:

So $p = 42$.

Use $x = 42$ in either line; $y = 3x - 2$ is easiest:

So $q = 124$ and the intersection point is $(p, q) = (42, 124)$.

Now add the coordinates:

Therefore, the value of $p + q$ is $166$.