Answer:
[tex]y=-\frac{1}{3} x+7[/tex]
Step-by-step 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.
[tex]x+3y=6\\\\3y=6-x\\\\y=2-\frac{1}{3} x[/tex]
Once we solve for y, we can see that the slope is [tex]-\frac{1}{3}[/tex]
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: [tex](y-y_1)=m(x-x_1)[/tex]
In this formula, m is the slope, [tex]x_1[/tex] is the x value of the coordinate pair, and [tex]y_1[/tex] 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.
[tex]y-5=-\frac{1}{3} (x-6)\\\\y-5=-\frac{1}{3}x+2 \\\\y=-\frac{1}{3}x+7[/tex]
