Question

What is the parallel line to y=-4x-5 and passes the point (-2,6)

Answer 1

Answer:

y = - 4x - 2 is the required equation of the line.

Step-by-step explanation:

Equation of two parallel lines differ only by a constant.

If the equation of a line is $ax + by + l = 0$ then the equation of the line parallel to it is given by $ax + by + k = 0$.

Note that only the constants differ in both the equations.

The given equation is: y = - 4x - 2

This is equivalent to 4x + y + 2 = 0.

Therefore, the equation of the line parallel to the given line will be:

4x + y + k = 0.

We are also given the point which passes through the line. We can substitute it to determine the value of 'k'.

Substituting (- 2, 6), we get:

4(-2) + 6 + k = 0

⇒ - 8 + 6 + k = 0

⇒ k = 2

Hence, the equation of the required line is: y = - 4x - 2