a)
The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m is the slope
c is the y intercept
The given equation of the line is
5x - 3y = 15
3y = 5x - 15
Dividing both sides by 3,
y = 5x/3 - 5
By comparing this equation with the slope intercept equation,
slope, m = 5/3
If two lines are parallel, it means that they have the same slope. This means that the slope of the line passing through the point (3/8, - 1) and parallel to the given line is 5/3
We would find the y intercept of the line by substituting m = 5/3, x = 3/8 and y = - 1 into the slope intercept equation. We have
- 1 = 5/3 * 3/8 + c
- 1 = 5/8 + c
c = - 1 - 5/8 = (- 8 - 5)/8
c = - 13/8
We would substitute m = 5/3 and c = - 13/8 into the slope intercept equation. Thus, the equation of the line is
y = 5x/3 - 13/8
b) If two lines are perpendicular, it means that the slope. This means that the slope of the line passing through the point (3/8, - 1) and perpendicular to the given line is - 3/5
We would find the y intercept of the line by substituting m = - 3/5, x = 3/8 and y = - 1 into the slope intercept equation. We have
- 1 = - 3/5 * 3/8 + c
- 1 = - 9/40 + c
c = - 1 + 9/40 = (- 40 + 9)/40
c = - 31/40
We would substitute m = - 3/5 and c = - 31/40 into the slope intercept equation. The equation of the line is
y = - 3x/5 - 31/40