Answer:
Equation of parallel line:
Equation of perpendicular line:
Explanation:
Parallel lines have same slope
Slope of y = -5x + 9 is -5
Parallel line will also have slope -5
Equation is y = -5x + b where b is the y intercept to be determined
Since line passes through (2, -4) these values of x and y must satisfy the equation for the parallel line
Plugging in we get
-4 = -5(2) + b
-4 = -10 + b
b = 10 - 4 = 6
Equation of parallel line is y = -5x + 6
Perpendicular lines have slope = negative of reciprocal of each other
Original line has slope -5
Perpendicular line will have slope -(-1/5) = 1/5
Equation of perpendicular line is
y = -1/5 x + b
Plugging in (2, -4)
=> -4 = 1/5(2) + b
=> -4 = 2/5 + b
==> -4 - 2/5 = b
b = -22/5
Equation of perpendicular line is
y = (-1/5)x - 22/5