1)
5x - 2y = 8
2y = 5x - 8
y = (5/2)x - 4
Thus, m = 5/2, since both lines are parallel.
Using the slope formula, we have:
(y + 3) / (x + 2) = (5/2)
(y + 3) = (5/2)(x + 2)
y + 3 = (5/2)x + 5
y = (5/2)x + 2
Thus, b = 2
2)
x - 2y = -3
2y = x + 3
y = (1/2)x + (3/2)
Thus, m = 1/2, since both lines are parallel.
Using the slope formula, we have:
(y - 2) / (x + 1) = 1/2
y - 2 = (1/2)(x + 1)
y - 2 = (1/2)x + (1/2)
y = (1/2)x + (5/2)
Thus, b = 5/2.
3)
y = 5x - 4
Since the two lines are perpendicular, m = -1 / (5) = -1/5
Using the slope formula, we have:
(y + 3) / (x - 5) = -1/5
y + 3 = (-1/5)(x - 5)
y + 3 = (-1/5)x + 1
y = (-1/5)x - 2
4)
A line perpendicular to another line with the form y = a, where a is any real number, will have to be of the form x = d, where d is some real number.
Thus, the line we need is x = 5, since it passes through (5,1) and is of the form x = d.
In this case, m = infinite and b does not exist, since x = 5 does not cut the y-axis.
5)
A line parallel to another line of the form x = a, where a is any real number, will be of the form x = d, where d is some real number.
Thus, the line we need is x = -2, since it is of the form x = d, and it passes through (-2,-7).
m is once again infinite, and b does not exist, since the line does not cut the y-axis.