GCSE Maths: Straight-Line Graphs

The straight line y = mx + c is the single most-used graph in GCSE Mathematics, and questions about it span every difficulty band — from reading a gradient straight off an equation to the Higher tier perpendicularity rule. This quiz covers that whole span in ten questions.

The early questions secure the fundamentals: identifying gradient and y-intercept from an equation, including the rearrangement case 2y = 4x + 10 where the equation must first be divided through before m and c can be read off — a step that costs marks every year when skipped. You will check whether given points lie on a line by substitution, and calculate a gradient from two coordinates using the change-in-y over change-in-x formula.

The middle of the set turns to constructing equations: finding the equation of a line from its gradient and a point on it, and building a linear model from a real context — a taxi fare with a fixed base fee plus a per-mile rate, the archetypal "interpret the gradient and intercept" exam scenario where m and c each carry physical meaning.

The Higher tier material closes the set with parallel and perpendicular lines: recognising that parallel lines share the same gradient regardless of their intercepts, and applying the negative reciprocal rule to find gradients perpendicular to 2 and to −¼. The distractors here are built from the two classic confusions — using the reciprocal without the sign change, and using the negative without the reciprocal.

Each question is fully self-contained with concrete coordinates, and every explanation walks through the standard method, making the set equally useful for first practice or final revision before the calculator paper.

• Read gradient and y-intercept from y = mx + c, rearranging the equation first when necessary
• Verify whether a point lies on a line by substitution
• Calculate a gradient from two points and construct the equation of a line
• Interpret gradient and intercept in real-life linear models
• Use gradient rules for parallel lines and the negative reciprocal rule for perpendicular lines (Higher)

Topic scope follows the Algebra strand of the Department for Education's GCSE mathematics subject content: using the form y = mx + c to identify parallel and (Higher) perpendicular lines, finding the equation of a line through given points, and interpreting gradients and intercepts of linear functions in real contexts.