Plotting Linear Graphs
This topic covers 5 learning steps, guiding your child from the basics through to confident problem-solving. Each step includes a worked example and adaptive practice questions.
What Your Child Will Learn
- y = mx + c basics
Identify gradient and y-intercept - Plot from equation
Plot a line from y = mx + c - Find equation from graph
Read gradient and intercept from a graph - Parallel & perpendicular
Understand parallel and perpendicular gradients - Intersection of lines
Find where two lines cross
Before This Topic
Your child should be comfortable with:
- Four-Quadrant Coordinates (Year 6)
- Linear Sequences (Year 6)
Common Mistakes
- Confusing the gradient (m) and the y-intercept (c) in y = mx + c (e.g. in y = 3x + 2, thinking the gradient is 2)
In y = mx + c, m (the number multiplied by x) is the gradient (steepness), and c (the number on its own) is the y-intercept (where the line crosses the y-axis). In y = 3x + 2, the gradient is 3 and the y-intercept is 2. - Calculating gradient as "across over up" instead of "up over across" (getting the fraction upside down)
Gradient = change in y ÷ change in x = rise ÷ run. Pick two points on the line: count how far UP (y), then how far ACROSS (x). If the line goes up 6 and across 2, the gradient is 6/2 = 3, not 2/6.
Tips for Parents
- Use a table of values to plot: choose x = -2, -1, 0, 1, 2, substitute into the equation to find y, then plot the points. They should form a straight line.
- Explain gradient using hills: "A gradient of 2 means for every 1 step forward, you go 2 steps up — quite steep. A gradient of 1/2 means every 2 steps forward, 1 step up — gentle." A negative gradient slopes downhill.
- Spot y = mx + c in real life: "A taxi charges £3 to start (that is c) plus £2 per mile (that is m). So the cost is y = 2x + 3." Plot it together.
- Practise reading equations from graphs: find where the line crosses the y-axis (that is c), then calculate the gradient between two clear points on the line.
Key Words
- Gradient — How steep a line is — calculated as change in y ÷ change in x. A gradient of 3 means the line goes up 3 for every 1 it goes across.
- y-intercept — Where the line crosses the y-axis — the value of y when x = 0. In y = 3x + 2, the y-intercept is 2.
- y = mx + c — The equation of a straight line, where m is the gradient and c is the y-intercept.
- Parallel lines — Lines that never meet — they have the same gradient but different y-intercepts.
- Perpendicular lines — Lines that cross at right angles — their gradients multiply to give -1.
Where This Fits
Before this topic: Children should be confident with coordinates in all four quadrants, substituting into expressions, and recognising linear sequences.
After this topic: Linear graphs lead to simultaneous equations (where two lines cross), quadratic and other non-linear graphs, and real-world modelling at GCSE.
How MathCraft Teaches This
In MathCraft, Plotting Linear Graphs is taught through the Coordinates & Statistics adventure track. Your child follows guided lessons with friendly characters, works through examples step by step, then practises with questions that adapt to their level.
The adaptive engine tracks mastery across all 5 steps, revisiting concepts your child finds tricky and advancing when they're ready. Parents can see detailed progress in the Parent Dashboard.
Practise Plotting Linear Graphs with MathCraft
Step-by-step lessons, worked examples, and adaptive practice — all wrapped in an adventure game your child will love.
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