The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m = slope
c = y intercept
The given equation is expressed as
y = 7x/3 + 5
By comparing both equations, slope,m = 7/3
Recall, if two lines are parallel, it means that they have the same slope. This means that the slope of the line parallel to the given line is 7/3. Since the line passes through the point(- 9, 2), to find the y intercept of this line, we would substitute m = 7/3, x = - 9 and y = 2 into the slope intercept equation. We have
2 = 7/3 * - 9 + c
2 = - 21 + c
c = 2 + 21 = 23
The equation of the parallel line is
y = 7x/3 + 23
Recall, if two lines are perpendicular, it means that the slope of one line is equal to the negative reciprocal of the slope of the other line. This means that the slope of the line perpendicular to the given line is - 3/7. Since the line passes through the point(- 9, 2), to find the y intercept of this line, we would substitute m = - 3/7, x = - 9 and y = 2 into the slope intercept equation. We have
2 = - 3/7 * - 9 + c
2 = 27/7 + c
c = 2 - 27/7
c = - 13/7
The equation of the perpendicular line is
y = - 3x/7 - 13/7