How do I turn this perpendicular line into standard form? y = -1/3x + 2/3

Question

I had to turn the equation, y - 3 = 3(x + 1), into a perpendicular line that passes through (5,-1) and I got y= -1/3x + 2/3 which I think is correct. I just don't know how to turn it into standard form now. 

Answer 1

   The line:   y-3 = 3(x+1)   or   y = 3x+4

You may (1) first find the equation of the perpendicular line that passes thru (5,-1), then convert it to Standard Form or (2) convert the equation to Standard Form, then find the equation of the line that passes thru (5,-1).  See if you can follow both methods:

 

Important:  If a line has slope m, then all perpendicular lines have a slope of  (-1/m).  That's called the negative reciprocal.

 

(1) find the equation in slope-intercept form, then convert to Standard Form

    The line:   y-3 = 3(x+1)   or   y = 3x+4

    Perpendicular line:    y = (-1/3)x + b     [and we need point (5,-1) to find b

                -1 = (-1/3)(5) + b

                -1 = -5/3 + b

                  2/3 = b

     The perpendicular line is:    y = (-1/3)x + 2/3

     The Standard Form of the equation of a line looks like:   Ax+By=C

          The perpendicular line is:

               (1/3)x + y = 2/3

                x + 3y = 2       [by convention, coefficient of x is positive; x is first;

                                          get rid of fractions]

 

(2) Convert to Standard Form, then find the specific equation

   The line:   y-3 = 3(x+1)   or   y = 3x+4

   In Standard Form:      3x - y = 4        [Note: slope is (-A/B) = (-3)/(-1) = 3

   Slope of all parallel lines:  (-1/3)   [that is, -A/B]

   Equation of parallel line:   x + 3y = D     [and we need point (5,-1) to determine D]

        5 + 3(-1) = D

           2 = D

   The parallel line, in Standard Form, is :     x + 3y = 2

Answer 2

Yes, you got the correct equation, but to convert it into standard form:

 

y = -1/3x + 2/3

1/3x + y = 2/3

 

You can go further and multiply everything by 3:

 

x + 3y = 2