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Solving and modelling with lines: cheat sheet

Linear relations · The words and methods from the lessons, with an example of each.

solve with a graph

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

2x+3=11  ⇒  x=42x + 3 = 11 \;\Rightarrow\; x = 4
y = 2x + 3 meets y = 11 at x = 4
y = 2x + 3 meets y = 11 at x = 4

rule from a situation

A starting amount plus a rate: the start is cc (4 dollars to get in) and the rate is mm (2 dollars per km).

T=2d+4T = 2d + 4

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 at g=45g + 20 = 40 \text{ at } g = 4