The standard form of a line:
[tex]Ax+By=C[/tex]
The point-slope form of a line:
[tex]y-y_1=m(x-x_1)[/tex]
We have the point (3, 5) and the slope m = 5/3. Substitute:
[tex]y-5=\dfrac{5}{3}(x-3)[/tex]
Convert it to the standard form:
[tex]y-5=\dfrac{5}{3}(x-3)[/tex] multioly both sides by 3
[tex]3y-15=5(x-3)[/tex] use distributive property
[tex]3y-15=5x-15[/tex] add 15 to both sides
[tex]3y=5x[/tex] subtract 3y from both sides
[tex]5x-3y=0[/tex]
