Question

What is the equation of a line, in general form, that passes through point (1, -2) and has a slope of 1/3

Answer 1

equation of a line that passes through the point (x1,y1) and has a slope of m is

y-y1=m(x-x1)

given

(1,-2) and slope of 1/3


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

general form is ax+by=c (or ax+by+c=0) where a,b,c are integers and a is positive


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

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

times both sides by 3

3y+6=x-1

minus 3y both sides

6=x-3y-1

add 1 both sides

7=x-3y

x-3y=7

To get ax+by+c=0 form, subtract 7 from both sides to get
x-3y-7=0