point-slope form

Point-slope form is the natural way to write a line when you know one point it passes through and how steep it is. It says, in effect: “start at this point, and the rest follows from the slope.”

If the line has slope m and passes through (x₁, y₁), its equation is y − y₁ = m(x − x₁). This comes directly from the slope formula: for any other point (x, y), the slope (y − y₁)/(x − x₁) must equal m, and clearing the denominator gives the form above.

It is the quickest starting point for many problems — given a point and a slope, just substitute. You can then rearrange into slope-intercept form (y = mx + b) or standard form whenever a tidier answer is wanted.