Question

What is an equation of the line that passes through the point (5,-3) and is parallel to the line x+5y=45?

Answer 1

`\btext{x+5y=-10}`

Explanation:

When two lines are parallel,their slopes are equal.

Given line is
`x+5y=45`.

Let
`m` be the slope of the line.

`m=-5`.

It is given that the line passes through the point
`(5,-3)`.

The equation of the line passing through
`(x_(1),y_(1))` and has slope
`m` is
`y-y_(1)=m(x-x_(1))`

`x_(1)=5`

`y_(1)=-3`

`m=-5`

So, the equation is
`y-5=-5(x+3)`

which simplifies to
`x+5y=-10`