For this case we have that by definition, the equation of the line in the slope-intersection form is given by:
Where:
m: It's the slope
b: It is the cut-off point with the y axis
By definition, if two lines are parallel then their slopes are equal.
We have the following line:
[tex]-x + 3y = 6\\3y = x + 6\\y = \frac {1} {3} x + \frac {6} {3}\\y = \frac {1} {3} x + 2[/tex]
Thus, the slope is:[tex]m_ {1} = \frac {1} {3}[/tex]
Then [tex]m_ {2} = \frac {1} {3}[/tex]
So, the line is of the form:
[tex]y = \frac {1} {3} x + b[/tex]
We substitute the point[tex](x, y) :( 3,5)[/tex]and find b:
[tex]5 = \frac {1} {3} (3) + b\\5 = b[/tex]
Thus, the equation is:
[tex]y = \frac {1} {3} x + 5[/tex]
Answer:
[tex]y = \frac {1} {3} x + 5[/tex]
