SL 2.1—Straight lines

A straight-line model can be written y=mx+c, where m is the gradient and c is the y-intercept. The gradient measures change in y per unit change in x.

Use the form that matches the data: two points give m=(y₂−y₁)/(x₂−x₁); a point and a gradient give y−y₁=m(x−x₁). Check the scale and units before interpreting m.

Through (2,5) and (6,13), m=8/4=2, so y−5=2(x−2), or y=2x+1. At x=0 the model predicts 1, not 0.

A negative gradient means y falls as x rises; it does not mean the intercept is negative. Do not swap coordinates or treat correlation as proof that the line is causal.

Line-form map: $y=mx+c$ shows gradient and $y$-intercept, $y-y_1=m(x-x_1)$ uses a known point, and $ax+by+d=0$ is general form. Set $y=0$ for the $x$-intercept and $x=0$ for the $y$-intercept. Parallel non-vertical lines have $m_1=m_2$; perpendicular non-vertical lines satisfy $m_1m_2=-1$. Vertical lines $x=k$ require a separate case because their gradient is undefined.