How can you tell they’ve got it: Linear Function Graphs?

If they’ve got it, you’ll see things like: Explain that changing m in y = mx + c alters the steepness and direction of the line; Identify the y-intercept of a line from its equation and from its graph; Determine whether a given equation will produce a straight line or a curve. Or just try it together: If your child sees the equation y = 2x + 3, can they explain what the graph will look like — including how steep it is and where it crosses the y-axis?

Mathematics Algebra Ages 12–14

Linear Function Graphs

Your child knows an equation like y = 2x + 3 makes a straight line. They can say how steep it is and where it crosses the y-axis.

In curriculum terms

Recognise that a linear function produces a straight-line graph, understand the relationship between an equation of the form y = mx + c and its graphical representation, and interpret gradient and y-intercept in context

Ages are typical, not deadlines — follow your child’s pace. How to help at home →

How to tell they’ve got it

Tick these off as you see them — no test required.

Explain that changing m in y = mx + c alters the steepness and direction of the line
Identify the y-intercept of a line from its equation and from its graph
Determine whether a given equation will produce a straight line or a curve

🖨 Print this page to keep the checklist — it prints beautifully.

Try this together

If your child sees the equation y = 2x + 3, can they explain what the graph will look like — including how steep it is and where it crosses the y-axis?

Where this sits on the map

Stuck here? Check the skills it builds on first. Confident? Here’s what it unlocks.

Builds on

Algebraic Transformationsages 11–13Recognising the relationship between y=mx+c and its graph requires moving fluently between algebraic and graphical representations

Coordinatesages 11–12Understanding linear graphs requires confident coordinate plotting

Substituting into Formulaeages 11–12Interpreting y = mx + c requires substitution to generate coordinate pairs

Linear Function Graphsthis skill · ages 12–14

Unlocks

Plotting Linear Graphsages 12–14Plotting linear graphs requires understanding what y = mx + c represents

Proportionages 12–14Graphical representations of proportion connect to linear graphs (y = kx through origin)

Ratio Notation and Relationshipsages 12–14Connecting ratios to linear functions links to understanding y = mx + c from algebra

Scatter Graphs & Correlationages 13–14Line of best fit connects to understanding linear relationships from y = mx + c

solid = must come firstdashed = helps

Curriculum alignment

Where this fits in the official school curriculum — our best automated guess, not yet checked by a person.

This skill sits beyond Year 6 in the Australian Curriculum, so no F–6 code is matched. It also sits beyond the NSW K–6 syllabuses. It also sits beyond Level 6 in the Victorian Curriculum.

Nearby on the map

Factorising Expressionsages 12–13 Nth-Term Rulesages 12–14 Plotting Linear Graphsages 12–14 Simple formulaeages 12–14

All Algebra skills →