Determine the slope and the y intercept of the line that is parallel to 3x-9y=11 if the point (1,3) is on this line .

We'll consider the given point located on the line whose
slope and y intercept have to be found out.

We'll recall
the fact that 2 lines are parallel when their slopes are equal. For this reason, we'll
put the given equation of the line in the point slope
form.

y = mx + b, m is the slope and b is y
intercept

For this reason, we'll subtract 3x both
sides:

-9y = 11 - 3x

We'll
divide by -9:

y = x/3 -
11/9

Comparing, we'll get the slope of the first line: m1 =
1/3

The slope of the parallel line is m2 =
1/3.

Since the line is passing through the point  (1;3),
the equation of the line is:

y - 3 = (1/3)*(x -
1)

We'll add 3:

y = (1/3)*(x -
1) + 3

We'll remove the
brackets:

y = x/3 - 1/3 +
3

We'll combine like terms:

y
= x/3 + 8/3

The requested slope and y
intercept of the line are:m=1/3 and b = 8/3.