How to write an equation in Ax+By=C given the slope and one set of coordinates?

I know that A,B, and C are supposed to become integers and that x and y should stay variables. But I'm not sure what A,B, and C represent. I mean, in y=mx+b I know that m is slope and b is the starting point, but what about with standard form? My teacher never clarified and this homework is crazy hard.





For example, I'm given





slope = -1


and goes through (4,-3)





So I need to write an equation in standard form. Also, on another problem, I'm just given this





x-intercept=2


y-intercept=5





and must write an equation for that in standard form. I'm not sure how to approach this. Please help.

How to write an equation in Ax+By=C given the slope and one set of coordinates?
given Ax+By=C, I rewrite it in slope-intercept form (y=mx+b)


y= C/B - A/Bx





you are given the slope, so you know "m" in "y=mx+b"


they give you a point on the line, so plug in the given values for "x" and "y" and solve for "b"