1.3.1—Straight lines

The gradient m measures change in y per unit change in x. A line can be written y=mx+c, y−y₁=m(x−x₁), or ax+by+c=0 depending on the information given.

Calculate m=(y₂−y₁)/(x₂−x₁), then substitute a known point to determine the intercept. Parallel lines have equal gradients; perpendicular non-vertical lines satisfy m₁m₂=−1.

Through (2,5) with gradient −3: y−5=−3(x−2), so y=−3x+11.

The intercept is not the y-coordinate of every point, and a vertical line has undefined gradient rather than gradient zero.