i need help on a Algebra problem!?

Question

**Write an equation for the line that is perpendicualr to the given line and that passes through the given point**
EQUATION 1. (-5,5) ; y=-5x+9
~ I understand how to find m but i dont know how to find b...~
**Write an equation for the line that is parallel to the given line and that passes through the given point**
EQUATION 2. (1,3) ; y=-4x+5

^^how would u do these if u were given A line instead of an equation??^^im confused please help!!!!

one more thing....
**Tell whether the lines for each pair of equations are parallel, perpendicular, or neither**
x=10
y=-2
(that's all it gave me nd im totally lost)
thnx so much

Answer 1

Parallel lines always have the same slope.
Perpendicular lines have slopes that are negative reciprocals (like 2/3 and -3/2).

For the first equation, the slope of the perpendicular line would be 1/5 (the negative reciprocal of -5). You can find the "b" by plugging in the numbers from the point you know for "x" and "y" in the formula y = mx + b
5 = 1/5(-5) + b
5 = -1 + b
6 = b
So the equation would be y = (1/5)x + 6

In the second equation, the slope of the parallel line would be -4.
Again you just plug in "x" and "y".
3 = -4(1) + b
3 = -4 + b
7 = b
So the equation would be y = -4x + 7

For your final question, x = 10 is a horizontal line and y = -2 is a vertical line. These would be perpendicular.

Answer 2

The first one is 1/5x+6 (perpendicular)
The second one is 4x-1 (parallel)
To get a perpendicular line, you you get the reciprocal of the slope and a different y intercept. For a parallel you get the same slope but different y intercept.