Question

Which of the following is the equation of a line parallel to the line y = 4x+1,passing through the point (5,1)?

Answer 1

The given eqation is:

`y=4x+1`

Notice that the slope of the line is 4

Recall that the slopes of parallel lines are equal

Hence the slope of the required line is 4.

Since the line passes through the point (5,1)

The equation is:

`y-1=4(x-5)`

This is simplified to give:

`\begin{gathered} y-1=4x-20 \\ y-4x=-20+1 \\ -4x+y=-19 \\ 4x-y=19 \end{gathered}`

Therefore the equation of the line is:

`4x-y=19`