In each case you are given the equation of a line and a point. The first three give the line in slope intercept form. To find the parallel or perpendicular line, just modify that equation thusly.
For parallel line, keep the slope the same, and change the intercept. Replace it with a variable, and replace the x and y with the values of the given point. Solve for the intercept.
For the perpendicular line, the procudure is the same, except change the slope to its negative reciprocal before finding the new intercept.
I'll do #4 as example. This one, the given equation is not already in slope intercept form, so we'll quickly do that.
3x - 2y = -8
subtract 3x from both sides, then divide both sides by -2
y = (-3x - 8)/-2 = 3x/2 + 4
so the parallel line passing through (3,-1) is
[-1] = (3/2)*[3] + b
I used square brackets to show where I substituted the x and y values
now solve this for b and you get
b = -1 - 9/4 = (-4-9)/4 = -13/4
hence
y = (3/2)x - 13/4
for the perpendicular line, we do the same thing except this time the slope will be -1/(original slope), in this case that is -1/(3/2) = -2/3
so the line is y = -2x/3 + b, and we need to substitute the point values to solve for b
[-1] = (-2/3)*[3] + b
hence
b = -1 + 2 = 1
so the perpendicular line is
y = -2x/3 + 1
