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
y = 2x/3 - 7
By comparing both equations,
m = 2/3
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 perpendicular line passing through the point (2, 6) is the negative reciprocal of 2/3. It is - 3/2
Thus, m = - 3/2
We would find the y intercept of the perpendicular line by substituting m = - 3/2, x = 2 and y = 6 into the slope intercept equation. We have
6 = - 3/2 * 2 + c
6 = - 3 + c
c = 6 + 3 = 9
By substituting m = - 3/2 and c = 9 into the slope intercept equation, the equation of the perpendicular line is
y = - 3x/2 + 9
Also,
If two lines are parallel, it means that the slope of one line is equal to the slope of the other line. This means that the slope of the parallel line passing through the point (2, 6) is 2/3
Thus, m = 2/3
We would find the y intercept of the perpendicular line by substituting m = 2/3, x = 2 and y = 6 into the slope intercept equation. We have
6 = 2/3 * 2 + c
6 = 4/3 + c
c = 6 - 4/3 = 14/3
By substituting m = 2/3 and c = 14/3 into the slope intercept equation, the equation of the parallel line is
y = 2x/3 + 14/3