Find the equation of the straight line passing through the point M (3; -5) which is parallel to the

Find the equation of the straight line passing through the point M (3; -5) which is parallel to the straight line x-3y + 9 = 0.

General view of the straight line y = kx + b. Finding the equation of the straight line is reduced to finding the coefficients k and b.

1) Finding k.

First, we bring the formula for the function x – 3y + 9 = 0 to the standard form y = kx + b:

x – 3y + 9 = 0

-3y = -x – 9

y = 1 / 3x + 3.

Since the required straight line is parallel to the straight line y = 1 / 3x + 3, it means that they have the same slope k = 1/3.

2) Finding b.

Substitute the coordinates of the point M (3; -5) and the found k into the general formula of the straight line y = kx + b:

-5 = 1/3 * 3 + b

b = -5 – 1/3 * 3 = -5 – 1 = -6.

Answer: y = 1 / 3x – 6.