---
title: "Solving and modelling with lines: cheat sheet"
subtitle: "Linear relations"
---

# Solving and modelling with lines

> The words and methods from this unit, with an example of each.

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**solve with a graph**: Draw each side as a line: $y = 2x + 3$ and $y = 11$. Where they meet, both sides are equal, so the $x$ there is the solution.

$$2x + 3 = 11 \;\Rightarrow\; x = 4$$

_y = 2x + 3 meets y = 11 at x = 4_

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:::keep-together

**rule from a situation**: A starting amount plus a rate: the start is $c$ (4 dollars to get in) and the rate is $m$ (2 dollars per km).

$$T = 2d + 4$$

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**comparing two plans**: Put both rules on one graph. Where the lines cross, the plans cost the same; on either side, the lower line is cheaper. Check where the model makes sense (no negative gigabytes).

$$5g + 20 = 40 \text{ at } g = 4$$

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