Graph Gallery
Walk the gallery of graphs: read coordinates, decode y = mx + c for gradient and intercept, spot parallel lines, and recognise every shape from a straight line to a parabola, cubic and reciprocal.
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Graph Gallery 🖼️
Every graph tells a story with a picture. In this gallery you will learn to read the **straight line** (y = mx + c) and to recognise the famous **curves** at a glance. Two skills carry most of the marks: pulling the **gradient** and **intercept** out of a line, and matching a **shape** to its equation.
Coordinates 📍
A point is written **(x, y)**: the first number is how far **across** (x), the second how far **up** (y). Both axes run negative as well as positive, giving **four quadrants**. So (3, −2) means 3 right and 2 down. Read across before up — "along the corridor, then up the stairs".
Plot the coordinate
An interactive activity.
The straight line: y = mx + c 📈
Every straight line can be written **y = mx + c**: • **m** is the **gradient** — how steep the line is. • **c** is the **y-intercept** — where the line crosses the y-axis. For **y = 2x + 3**, the gradient is 2 and the line crosses the y-axis at 3. Read them straight off the equation.
Gradient = rise over run 📐
The **gradient** measures steepness: **gradient = rise ÷ run** (how much it goes **up** for each step **across**). • A line going **uphill** left-to-right has a **positive** gradient. • A line going **downhill** has a **negative** gradient. It is rise ÷ run — never run ÷ rise. Up over across.
Gradient from two points
An interactive activity.
Find the y-intercept
For the line y = 3x − 4, where does it cross the y-axis (the value of c)?
- −4
- 3
- 4
- 0
Read the gradient
An interactive activity.
Parallel lines ⏸️
Two lines are **parallel** when they have the **same gradient** — the same value of **m**. Their intercepts (c) can differ; only the steepness must match. So y = 2x + 1 and y = 2x − 3 are parallel (both gradient 2), but y = 3x + 1 is not.
Which line is parallel?
Which of these lines is parallel to y = 2x + 1?
- y = 2x − 3
- y = 3x + 1
- y = −2x + 1
- y = ½x + 1
The shapes of graphs 🎨
Not every graph is a line. Learn these four silhouettes: • **Linear** (y = mx + c) — a straight line. • **Quadratic** (y = x²) — a U-shaped **parabola**. • **Cubic** (y = x³) — an S-shaped curve. • **Reciprocal** (y = 1/x) — two separate curved branches.
Find the parabola
An interactive activity.
Match each equation to its graph shape
- y = 2x + 1
- y = x²
- y = x³
- y = 1/x
- A straight line
- A U-shaped parabola
- An S-shaped cubic curve
- A reciprocal with two branches
Name the shape
What shape is the graph of y = x² − 4?
- A parabola (U-shaped)
- A straight line
- An S-shaped cubic
- A reciprocal curve
Order the method
An interactive activity.
The equation of a line
A straight line has equation y = mx + c. The letter m is the _____, found as rise ÷ run, and the letter c is the _____, where the line crosses the y-axis. Two lines are parallel when they have the same _____.