Write one equation of a line that is parallel to and one equation of a line that is perpendicular to the graph of the line 11x-6y=21

Question

Writing an equation of a line

 

Answer 1

The equation 11x-6y=21 is in Standard Form.  You may convert Ax+By=C once and forever to slope-intercept form (y=mx+b) and find that the slope is (-A/B).

 

A line that is parallel has the same slope -- An example equation would be:   11x-6y=0    (slope=11/6)

 

A line that is perpendicular has a slope that is the negative reciprocal (that is, B/A).

    An example would be:  6x+11y=0     (slope=-6/11)

Answer 2

Solve the equation for y:

 

y = (11/6)x -7/3  Therefor the graph of the line has a slope of 11/6 and a y-intercept of -73.

 

To write a parallel line, use the same slope and a different y-intercept, such as:

 

y = (11/6)x + 1

 

To write a perpendicular line, take the negative reciprocal of the original slope and choose any y-intercept:

 

y= (-6/11)x + 1

Answer 3

Hi Ashley,

 

To answer this question, you need to remember two things:

 

(1) slopes of parallel lines are identical and

 

(2) the slope of a second line perpendicular to the first is the negative reciprocal of the first line (e.g., if the slope of the first line is 2 then the slope of the second line is -1/2)

 

Now, rewrite the equation in question in slope-intercept form (y = mx + b):

 

11x - 6y = 21

 

11x - 11x - 6y = 21 - 11x

 

-6y = -11x + 21 (reorganizing)

 

-6y/-6 = -11x/-6 + 21/-6

 

y = 11/6x - 21/6

 

So, the slope of the line is 11/6

 

Then, any equation with the same slope (e.g., y = 11/6x) is parallel to it.

 

Finally, any line perpendicular will have a slope that's the negative reciprocal of 11/6 or -6/11.

 

So, one perpendicular line (out of many) would be y = -6/11x

 

Hope this helps!

 

 

Answer 4

Let us change this to the form

 

y = mx + b

 

-6y = -11x + 21

 

y = (11/6)x - 21/6 = (11/6)x - 7/2

 

To get a parallel line, you need the same slope m = 11/6, so just change the constant -7/2 to any other number, say 0, for example:

 

y = (11/6)x

 

has the same slope, and therefore is parallel to, y = (11/6)x - 7/2

 

To get a perpendicular line to a line of slope m, you need a slope m' such that mm' = -1.  So any line of slope

 

m' = -1/m = -6/11 will be perpendicular to a line of slope 11/6.

 

y = (-6/11)x

 

is an example.