standard form of a line

Standard form writes a line as Ax + By = C, with the x and y terms lined up on the left and a constant on the right. It is the “balanced ledger” look — neat, symmetric, and good for comparison.

Usually A, B, and C are integers and A is taken non-negative. Unlike slope-intercept form, standard form can describe every line, including vertical ones: a vertical line is just 1·x + 0·y = C, i.e. x = C. The intercepts are easy here too — set y = 0 to find the x-intercept, set x = 0 to find the y-intercept.

When you need the slope, convert: solving Ax + By = C for y gives y = (−A/B)x + C/B, so the slope is −A/B (provided B is not 0). If B = 0 the line is vertical and has no slope.