Find the equation of a line parallel to y = -5x + 4 and passing through a point (-1, 4).

Linear equations and straight lines form an integral part of mathematics. They are used in various applications in many fields. By using its properties, we can find the equation of a line parallel to another line and passing through a particular point. Let's see how with the help of an example.

Answer: The equation of a line parallel to y = -5x + 4 and passing through a point (-1,4) is y = -5x - 1.

Let's understand how we arrived at the solution.

Explanation:

We know that two parallel lines have an equal slope. We use that property of straight lines to solve this problem.

The slope of y = -5x + 4 is -5.

Therefore, the equation for the family of lines parallel to y = -5x + 4 is y = -5x + c, where c is an arbitrary constant.

To find the value of c, replace the variable with point (-1, 4).

Therefore, we get 4 = -5(-1) + c.

Hence, c = -1.

Now, we replace c with -1 in the equation of the family of lines found earlier.

Therefore, The equation of a line parallel to y = -5x + 4 and passing through a point (-1, 4) is y = -5x - 1.