Solve for y = mx + b or y - y1 = m (m - x1). Your line will be in slope intercept form.
Now add/subtract/multiply/divide in order to get to Ax + By = C, where A,B&C are non-fractions and A>0.
For example: Write the equation of a line in standard form that has a slope of 4 and passes through (-3,5).
y - y1 = m (x - x1)
y - 5 = 4 (x - (-3))
y - 5 = 4x + 12
Add 5 to both sides.
y = 4x + 17
Subtract 4x from both sides to get the variables on the same side.
-4x + y = 17
The pattern for Standard Form shows that the coefficient with x can't be negative when it expresses A>0. So, multiply everything by -1, keeping in mind you can do anything to an equation and it will remain true as long as you do it to both sides.
-1(-4x + y = 17)
4x - y = -17