First, put the original equation into slope-intercept form, or y=mx+ b, where m is the slope and b is the y-intercept. If you don't know about slope-intercept form, read about it on Purple Math: https://www.purplemath.com/modules/strtlneq.htm, or watch a video on Khan Academy:

https://www.khanacademy.org/math/algebra/two-var-linear-equations/slope-intercept-form/v/slope-intercept-form

Starting with -4x-9y=2, add 4x to both sides to get

-9y=4x+2.

Divide every term by (-9) to get

y=(-4/9)x -2/9

This is slope intercept form, so we see that the slope, or m, of the given line is -4/9.

Parallel:

Parallel lines never run into each other, so they have to have the same slope, right? So m of the parallel equation, let's call it m_{2}, is also -4/9. Our equation so far for the second line is

y_{2}=(-4/9)x+b.

(5, -1) is a point on the line, so plug these in for x and y to find b: -1= (-4/9)5 +b. Converting -1 to -9/9 and multiplying (-4/9) by 5, we get

-9/9 = -20/9 +b.

Add 45/9 to both sides to get b =11/9. Plug in m and b to get the line of the parallel equation:

**Parallel: y=(-4/9)x+11/9**

*For the Perpendicular line:*

The slope of lines that are perpendicular are __negative reciprocals__ of each other. So, change the sign, and flip the fraction. If the first slope is 4, the perpendicular slope is -1/4. Our original slope is -4/9, so the slope of any line perpendicular to that is positive 9/4.

For the third (perpendicular) equation, we start with y_{3}=(9/4)x+b.

Again, plug (5, -1) in for x and y: -1=(9/4)5 +b.

Multiply on the right side: -1=45/4 +b, and change -1 to -4/4:

-4/4=45/4 +b, and subtract to get -49/4=b.

Plug in the new m and b to get the third equation:

**Perpendicular: y=(9/4)x - 49/4**

I hope that helps! Slope-intercept form is the best! It's super simple to work with!

Good luck in your math class!