MYP Maths: Linear Functions & Gradients FAQ

A linear function describes a straight-line relationship where y changes by the same fixed amount for every unit increase in x — that fixed amount is the gradient. In MYP 4-5 you'll write it as $y=mx+c$, with m as the gradient and c as the y-intercept, sitting inside the IB's Algebra branch of the mathematics framework.

Gradient measures steepness — how much y rises or falls for every one unit x increases. Given two coordinates $(x_1,y_1)$ and $(x_2,y_2)$, use $m=\frac{y_2-y_1}{x_2-x_1}$. A positive gradient slopes upward left to right, negative slopes downward, zero is horizontal, and an undefined gradient means a vertical line.

The equation $y=mx+c$ describes every point on a straight line. m is the gradient — how steep the line is and whether it rises or falls left to right. c is the y-intercept — where the line crosses the y-axis, the value of y when x equals zero.

Calculate the gradient first using $m=\frac{y_2-y_1}{x_2-x_1}$, then substitute either point into $y=mx+c$ to solve for c. Write your final equation in full and verify it by plugging in the second point — if both sides match, your equation is correct.

Read the question type first — are you given two points, a point plus a gradient, or a graph? Pick the right method: calculate m with $m=\frac{y_2-y_1}{x_2-x_1}$, substitute a known point into $y=mx+c$ to find c, then write the full equation. Always check your answer against the original data before moving on.

The three I see most often in MYP 4-5 mock papers: swapping the x and y values inside the gradient formula, dropping the negative sign when a line slopes downward, and confusing gradient (m) with y-intercept (c) when writing the final equation. All three are avoidable once you label your values clearly before substituting.

Real-life graphs — phone plans, distance-time, cost functions — test whether you can connect the maths to context, not just calculate it. Identify what the gradient represents (usually a rate, like cost per minute) and what the y-intercept represents (a fixed starting value, like a connection fee), then state both using the units given in the question.

Linear functions and gradients get assessed across all four MYP Mathematics criteria: Criterion A (Knowing and Understanding) tests calculations like finding m and c; Criterion B (Investigating Patterns) asks you to spot a linear rule from a table or sequence; Criterion C (Communicating) checks your working and notation; Criterion D (Applying Mathematics in Real-Life Contexts) uses linear models in context.

Expect command terms like calculate (a numerical answer with working shown), determine (find the correct answer using a clear method), sketch (an approximate graph with key features labelled, not drawn to scale), and justify (give valid reasons supporting your conclusion). Match the length and depth of your answer to the term used, not to how much space is on the page.

Both, usually — many MYP 4-5 teachers set an early non-calculator check on the gradient formula itself, then allow calculators for context-heavy Criterion D tasks involving decimals. If your school runs the IB's on-screen MYP eAssessment, an onscreen calculator is available throughout, so clear method and correct units matter more than raw calculation speed.

Everything you learn about gradients, y-intercepts and linear models in MYP 4-5 becomes the foundation for DP Mathematics: Analysis and Approaches and Applications and Interpretation, where linear functions reappear in coordinate geometry, linear regression and rates of change — an early step towards differentiation. Get the gradient formula solid now; it saves real time in the DP.

Extended mathematics doesn't reinvent linear functions — the core gradient formula and $y=mx+c$ are identical in both courses — but extended classes move faster and connect linear functions to harder material sooner, like simultaneous equations and quadratic-linear intersections. Standard mathematics spends longer consolidating the basics before adding complexity, which suits students who need more practice time to feel confident.

You don't need to remember the formulas yourself — the most useful thing you can do is ask your child to explain their working out loud, step by step. If they can't explain why they substituted a point into $y=mx+c$, that's usually where the gap is, not in the arithmetic itself.

Look for resources structured around the actual MYP criteria, not generic algebra drills — topical worksheets mixing calculation with real-life context questions, past-style Criterion B pattern tasks, and revision notes that separate 'find the gradient' from 'interpret the gradient' as distinct skills. That separation matters more for final grades than sheer volume of practice.