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 .
The slope of two parallel lines is the same. For the line 3x - 9y = 11, we can write it as
9y = 3x -11
=> y = x/3 - 11/3
This is in the slope intercept form with the slope equal to 1/3.
A line that passes through (1,3) and with a slope 1/3 is:
(y - 3)/(x - 1) = 1/3
=> 3y - 9 = x - 1
=> 3y = x + 8
=> y = x / 3 + 8/3
The y-intercept here is 8/3.
The required slope of the line is 1/3 and the y-intercept is 8/3.
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.