Answer:
Equation of parallel line: y = 3x/2 + 15
Equation of perpendicular line: y = - 2x/3 - 7/3
Explanation:
The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m represents slope
c represents y intercept
The equation of the given line is
y = 3x/2 + 3
By comparing with the slope intercept equation,
slope, m = 3/2
Recall, if two lines are parallel, it means that they have the same slope. Thus, the slope of the parallel line passing through the point, (- 8, 3) is 3/2. We would find the y intercept, c by substituting m = 3/2, x = - 8 and y = 3 into the slope intercept equation. We have
3 = 3/2 * - 8 + c
3 = - 12 + c
c = 3 + 12 = 15
By substituting m = 3/2 and c = 15 into the slope intercept equation, the equation of the parallel line passing through the point, (- 8, 3) is
y = 3x/2 + 15
Recall, if two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line. Thus, the slope of the perpendicular line passing through the point, (- 8, 3) is - 2/3. We would find the y intercept, c by substituting m = - 2/3, x = - 8 and y = 3 into the slope intercept equation. We have
3 = - 2/3 * - 8 + c
3 = 16/3 + c
c = 3 - 16/3 = - 7/3
By substituting m = - 2/3 and c = - 7/3 into the slope intercept equation, the equation of the perpendicular line passing through the point, (- 8, 3) is
y = - 2x/3 - 7/3