Plotting Equations of Proportionality Slideshow 27, Mathematics Mr Richard Sasaki

Objectives Review key graph elements Naming and showing co-ordinate points Be able to draw and name simple linear graphs.

Graph Elements Where is this? Origin (3.5, 3) Title (for example 𝑦=𝑎𝑥) 𝑥-axis 𝑦-axis Gridlines Values of 𝑦 Values of 𝑥

Graph Quadrants 𝐼𝐼 𝐼 𝐼𝐼𝐼 𝐼𝑉 𝑥≤0 𝑦≥0 𝑥≥0 𝑦≥0 𝑥≤0 𝑦≤0 𝑥≥0 𝑦≤0 Note: Try to remember this! Let’s look at the ranges of values for 𝑥 and 𝑦 in each quadrant of the graph anticlockwise. Each of the quadrants (sections out of four) are named…. 𝑥≤0 𝑦≥0 𝑥≥0 𝑦≥0 𝐼𝐼 𝐼 𝑥≤0 𝑦≤0 𝑥≥0 𝑦≤0 𝐼𝐼𝐼 𝐼𝑉

Graph Elements When plotting points on graph, you may need to show which is where with labels. For this, we need some new notation. If we want to name this point, P, how would we do that? P (4, 2) 𝑥 co-ordinate 𝑦 co-ordinate We can now give different points, different names.

Plotting Points Let’s plot some named co-ordinates on the graph below. 𝐴 ∙ 𝐺 ∙ 𝐹(2, 3) 𝐺(0, 8) 𝐻 ∙ 𝐻(−3, 6) 𝐼(−6, −7) 𝐵 ∙ 𝐹 ∙ Write down the points in red. 𝐷 ∙ 𝐴(−6, 9) 𝐵(4, 4) 𝐶 ∙ 𝐸 ∙ 𝐶(5, −2) 𝐷(0, 2) 𝐸(−1, −4) 𝐼 ∙

Answers – Part 1 𝐹 ∙ 𝐺 ∙ 𝐵 ∙ 𝐸 ∙ 𝐴 ∙ 𝐷 ∙ 𝐽 ∙ 𝐶 ∙ 𝐼 ∙ 𝐻 ∙ 2 2 16 4 2 2 16 4 −14−2 −18 0 −6 −20 16 −16 2 5 11 5 18 20 1 −11

Answers – Part 2 (3, 3), (3, −3), (−3, −3), (−3, 3) (0, 3), (3, 0), (0, −3), (−3, 0) 2.5 (𝑠𝑞𝑢𝑎𝑟𝑒 𝑢𝑛𝑖𝑡𝑠) 9𝜋 4 (𝑠𝑞𝑢𝑎𝑟𝑒 𝑢𝑛𝑖𝑡𝑠) 27 2 (𝑠𝑞𝑢𝑎𝑟𝑒 𝑢𝑛𝑖𝑡𝑠)

Drawing Graphs When we plot a linear graph… How many points (minimum) do we actually need? It’s a straight line…so only two! If there’s only two, it should be easy to draw without plotting points.

Drawing Graphs When drawing graphs in the form 𝑦=𝑎𝑥, the line always passes through the . origin The graph shown is . 𝑦=3𝑥 This means as 𝑥 increases by 1, 𝑦 increases by . 3 3 1 This is the case anywhere along the line. Note: 𝑦=𝑘𝑥 is not common with graphs.

Drawing Graphs So if we draw some graph 𝑦=𝑎𝑥, it passes through the origin, and if we increase 𝑥 by 1, we increase 𝑦 by . 𝑎 ∙ Let’s draw 𝑦=5𝑥. We know the line passes through (0, 0)… ∙ And if we increase 𝑥 by 1, we increase 𝑦 by . 5 Now we can draw our line!

2𝑥 −3𝑥 𝑥 4 The relationship is not linear. The rate of change changes. A horizontal line. Almost vertical, very, very steep and positive.