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.
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.