Write the equation of the line with slope m=2/3 and y intercept b=-8

The equation of the line with slope m and y intercept c is
y = mx+c. The line is inclined  to x axis with a slope  of arctanm  and  intersects  y
axis at c units from the origin.

Given m = 2/3 and c =
-8.

So substituting the values of m and c  in y = mx+c, we
get:

y = (2/3)x+(-8)
.....(1)

y = (2/3)x - 8. is the required equation in slope
intercept form. We can write this in ax+by+k = 0 form
also.

(1)*3 gives:

3y =
2x-8*3

3y = 2x-24.

Subtract 3y
and rearrrange:

2x-3y-24 = 0 which is in the standard
ax+by+k = 0 form.