Write an equation of the line that passes through point P and is parallel to the line with the given equation: P(2,5) Y-1=4x​

Given:

The equation of a line is:

A line parallel to the above line passes through the point P(2,5).

To find:

The equation of the parallel line.

Solution:

The slope intercept form of a line is:

        ...(i)

Where, m is the slope and b is the y-intercept.

The given equation is:

It can be rewritten as

       ...(ii)

On comparing (i) and (ii), we get

It means the slope of the given line is 4.

We know that the slopes of two perpendicular lines are equal. So, the slope of the required parallel line is also 4.

The parallel line passes through the point P(2,5) with slope 4, thus the equation of the parallel line is

Therefore, the equation of the required parallel line is .