Question 644646
you have to know a few things:
two forms of an equation of a line:
y = mx + b (slope-intercept form)
where
m is slope
b is y-intercept at (0,b)
.
y-y1 = m(x - x1) (point-slope form: used to derive equation of a line give one point and the slope)
.
if two lines are "parallel" their slopes are equal
.
if two lines are "perpendicular" their slopes are "negative reciprocal" (equals -1 when multiplied together)
.
.
4. through (-8,8) and parallel to y = 3/2x -3. 
slope of new line is 3/2
crossing (-8,8)
plug into "point-slope" form:
y-y1 = m(x - x1)
y-8 = (3/2)(x - (-8))
y-8 = (3/2)(x + 8)
y-8 = (3/2)x + (3/2)8
y-8 = (3/2)x + 12
y = (3/2)x + 20 (answer in "slope-intercept" form)
.
5. through (-3,8) and vertical
x = -3
.
6. through (-7,5) and perpendicular to y=2/3x -2 
since slope of:
y=2/3x -2
is 2/3.
Our new slope is -3/2 (because -3/2 * 2/3 = -1)
crossing (-7,5)
plug into "point-slope" form:
y-y1 = m(x - x1)
y-5 = (-3/2)(x - (-7))
y-5 = (-3/2)(x + 7)
y-5 = (-3/2)x + (-3/2)7
y-5 = (-3/2)x - 21/2
y = (-3/2)x - 21/2 + 5
y = (-3/2)x - 21/2 + 10/2
y = (-3/2)x - 11/2 (answer in "slope-intercept" form)