Question

What is an equation of the line that passes through the point (6,5) and is parallel to the line x+3y=6 ?

Answer 1

Check picture for answer

Answer 2

`y=-(1)/(3) x+7`

Explanation:

As we know that the line is parallel to the line x+3y=6, we know that it will have the same slope as this equation. To find the slope, we will need to solve for y.

`x+3y=6\\\\3y=6-x\\\\y=2-(1)/(3) x`

Once we solve for y, we can see that the slope is
`-(1)/(3)`

Now that we have the slope and a point, we can use the point-slope formula to find the equation of the line.

This formula says:
`(y-y_1)=m(x-x_1)`

In this formula, m is the slope,
`x_1` is the x value of the coordinate pair, and
`y_1` is the y value of the coordinate pair. Knowing this, we can plug in our three known variables into the equation to find the slope of the line.

`y-5=-(1)/(3) (x-6)\\\\y-5=-(1)/(3)x+2 \\\\y=-(1)/(3)x+7`