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 .

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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.

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