Two points fix a line, and turning them into y = mx + b is a real two-step: the slope has to be found before the intercept can be. These free printable worksheets give two points and ask for the whole equation.
Kid stuck on one? You don’t just get the sheet.
The answer key prints on a separate page.
The slope comes first, as (y₂ − y₁) ÷ (x₂ − x₁): for (1, 3) and (3, 7) that is (7 − 3) ÷ (3 − 1) = 2. Then one of the points goes back in to back out the intercept — 3 = 2 · 1 + b gives b = 1 — so the line is y = 2x + 1. Where the combined writing-linear-equations sheet also offers the easier slope-and-a-point questions, this page uses two points every time, so the slope step is never skipped.
The order is the whole discipline: a child who reaches for the intercept before the slope has nothing to substitute, because b depends on m. Every step-by-step walk here finds the slope, then substitutes a point, then reports both — and a child who stops at the slope has only half an answer.
One question from this sheet, worked through a step at a time.
Write the equation of the line through (2, 3) and (4, 5)