What is the standard form of a line through ( 6,-3) with a slope of 2/3?

Question

I don't understand this

Answer 1

 

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

 

The slope-intercept form of the equation of line looks like: y=mx+b,  where m is the slope.  Solving the equation above for y, you find that m=-A/B.

 

That means that the Standard Form of the equation of a line with slope of 2/3 is:

         2x - 3y = C      and we need a point, like (6,-3), to find C

 

         2(6) - 3(-3) = C

          12 + 9 = C

             21 = C

 

The Standard Form of the equation of a line that passes through point (6,-3) with slope m=2/3 is:

         2x - 3y = 21

 

To check slope:

        y = (2/3)x -7

To check point (6,-3):

        2(6) -3(-3) = 21   ?

          12 + 9 = 21   ?

               21 = 21? yes, that point is on the line

Answer 2

Point slope form of a line is 2/3 = (y-(-3))/x-6). Use algebra to find y = mx+b