Question

Write an equation of the line that passes through (4,−1) and is parallel to the line y=3x+7.

Answer 1

`$ y = 3x - 13 $`

Explanation:

The equation of parallel line differ only by their constant.

Hence, the equation of the line parallel to
`$ y = 3x + 7 $` is nothing but
`$ y = 3x + c $`.

When a point passing through this line is given we can substitute the point in this line and get the value for
`$ c $`.

The line passes through
`$ (4, -1) $`.

Therefore, we have:
`$ -1 = 3(4) + c $`

`$ \implies c = -13 $`.

Substituting this we get the equation of the parallel line as
`$ y = 3x - 13 $`.