How do I write an equation of a line with the general linear equation?

Question

Write the equation of te perpendicular to x+√3y=3 through the point (0,0).

Answer 1

The General Form of a linear equation looks like:

     Ax + By + C = 0

 

The Standard Form of a linear equation looks like:

     Ax + By = C        

 

(note: the values for A,B,C are not the same in these two lines.)

 

However, the wonderful thing about either the General Form or the Standard Form is that the slope is:

       -A/B           (you may put the equation into slope-intercept form to verify this)

 

Then, the second wonderful thing is that all perpendicular lines have a slope that is the negative reciprocal of the slope of the original line.  That is. when the line is written in General Form or Standard Form, the slope of the perpendicular line is:

       B/A

 

PLZ work this out using the slope-intercept form, then memorize it -- it will save you lots of work!

 

O.K. the original line is:                                  x+√3y=3

   the perpendicular line we are seeking is:      -√3x + y = D    

                           [we need the point (0,0) to determine which perpendicular line]

Putting (0,0) into this equation, we get 0+0=D,  so the perpendicular line has the equation:

      -√3x + y + 0 = 0  in General Form and

      -√3x + y = 0  in Standard Form

Answer 2

Hi Lyvvi,

 

Let's begin by transforming our given equation into the slope-intercept form of a linear equation, which is

y = mx + b (m is slope and b is y-intercept):

    x + √3y = 3

    √3y = -x + 3

        y = -x/√3 + 3/√3

 

We can see that the slope of given line is -1/√3.

 

The slope of the perpendicular line will be the negative reciprocal of the slope of the given line (√3).

 

Now we can plug in the coordinates of the given point through which the perpendicular line must pass and calculate the y-intercept (b):

    y = mx + b

    0 = √3(0) + b

    b = 0

 

Now we can write the equation of the line, which is perpendicular to the given line and also passes through the origin (0,0):

    y = mx + b

    y = √3x + 0

    y = √3x

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.