need help with standard form

Question

Write the standard form of the line that contains a slope of 2/3 and passes through the point (1, 1)

Answer 1

y-y(1)=m(x-x(1))

y-1=(2/3)(x-1)

y-1=(2/3)x-(2/3)

y=(2/3)x+1-(2/3)

y=(2/3)x+(1/3)

3y=2x+1

3y-2x=1

-2x+3y=1

2x-3y=-1

Answer 2

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

 

Now, once and forever, convert that to the slope-intercept form and find that the slope is:    -A/B

 

So, given a like with slope of 2/3, so far, we have:   -2x + 3y = C   and we need point (1,1) to find C.

       -2(1)+3(1) = C

                1 = C

The equation is:      -2x + 3y = 1,    however, by convention, the x-coefficient is positive, so multiply by (-1):

       2x - 3y = -1