Graphs summary

Key learning points

• Gradient $m=\frac{y_2-y_1}{x_2-x_1}$; intercept is where the line meets the $y$-axis.
• $y=mx+c$ is the standard straight-line form.
• Plot carefully: scale axes evenly and label.

Worked example 1 — Gradient

Through $(1,2)$ and $(3,8)$. Gradient?

Working

Rise over run.

Worked example 2 — Y-intercept

$y=3x-4$ meets the $y$-axis where?

Working

Set $x=0$.

Worked example 3 — Evaluate

For $y=2x+1$, find $y$ when $x=3$.

Working

Substitute.

Scaffolded Learning Sheet and answers (PDFs)

This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.