Question

what is the equation of a line that is parallel to y=4/7x−3 and passes through (14,4) ? Enter your answer in the box.

Answer 1

`y=(4)/(7)x-4`

Explanation:

1. Find the slope of the parallel line.

The general form to the equation of the line is given by
`y=mx+b` where m is the slope.

If you need to find a parallel line it has the same slope.

As the problem gives the equation of the line
`y=(4)/(7)x-3` it means that the slope of the line and its parallel is
`m=(4)/(7)`.

2. Find the equation of the parallel line.

The line must pass through the point (14,4).

Let´s name it as:

`x_(1)=14`

`y_(1)=4`

Replacing these values in the point-slope equation we have:

`y-y_(1)=m(x-x_(1))`

`y-4=m(x-14)`

`y-4=(4)/(7)(x-14)`

Solving for y:

`y-4=(4)/(7)x-(56)/(7)`

`y-4=(4)/(7)x-8`

`y=(4)/(7)x-8+4`

`y=(4)/(7)x-4`