Question

Could someone please answer this correctly?

Answer 1

Answer:

Equation of parallel line:
$y = -5x + 6$

Equation of perpendicular line:
$y = \dfrac{1}{5}x - \dfrac{22}{5}$

Step-by-step 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