If two lines are parallel, then they have the same slope. So, the slope of the line we are looking for needs to be 4. We can start by writing a point-slope equation:
y - y1 = m(x - x1)
We can substitute the values we have, the point we are using is (8, 5) because it needs to be on the line:
y - 5 = 4(x - 8)
We can distribute:
y - 5 = 4x - 32
y = 4x - 27
We are not given the slope-intercept form, so we must divide both sides by two to get it:
y = 1/4 x + 8
A perpendicular line has the slope that is the negative reciprocal of the one that is given. So, the slope of the line would be - 4. We can start by writing a point-slope equation:
y - y1 = m(x - x1)
We can substitute the values we have, the point we are using is (-5, 5) because it needs to be on the line:
