what is the equation in standard form of the line that passes through the point (4,-8) and has a slope 1/4?

Question

what is the equation in standard form of the line that passes through the point (4,-8) and has a slope 1/4?

Answer 1

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

 

Now, once and forever, convert that to the slope-intercept form of the equation of a line (y=mx+b) and remember that the slope, m, is (-A/B).  However, if you insist, this equation converts to:  y = (1/4)x - 9.

 

This problem gives the slope, m=1/4.  That means that the equation has the form:  x-4y=C  [since: -1/(-4) = 1/4] and we need point (4,-8) to find C:

       4-4(-8)=C

       4+32=C

        36=C

 

The equation of the line, in Standard Form, is: x-4y=36.

 

Check [Is the point (4,-8) on the line?]:

  Is   4 - 4*(-8)=36    ?

        4 +32 = 36   ?

         36 = 36  ?yes

Answer 2

y + 8 = 1/4 ( x - 4)

 

y + 8 = x / 4 - 1

 

y = x / 4 - 9

 

The equation of the line in standard form is 

 

y = (x / 4) - 9