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Starter

This lesson evaluates the equation of straight lines in a coordinate grid and explores the concepts of parallel lines and their equations. It includes examples and exercises for drawing graphs of functions.

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Starter

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  1. Starter Evaluate the following: y = 4x + 1 when x = -3 y = -3x – 2 when x = 5 y = x + 12 when x = -2 y = -9x – 22 when x = - 7

  2. Using a coordinate grid Coordinates are plotted on a grid of squares. 4 The x-axis and the y-axis intersect at the origin. y-axis 3 2 origin The lines of the grid are numbered using positive and negative integers as follows. 1 x-axis 0 –4 –3 –2 –1 1 2 3 4 –1 –2 The coordinates of the origin are (0, 0). –3 –4

  3. Graphs parallel to the y-axis y x What do these coordinate pairs have in common? (2, 3), (2, 1), (2, –2), (2, 4), (2, 0) and (2, –3)? The x-coordinate in each pair is equal to 2. Look what happens when these points are plotted on a graph. All of the points lie on a straight line parallel to the y-axis. Name five other points that will lie on this line. This line is called x = 2. x = 2

  4. Graphs parallel to the y-axis y x All graphs of the form x = c, where c is any number, will be parallel to the y-axis and will cut the x-axis at the point (c, 0). x = –10 x = –3 x = 4 x = 9

  5. Graphs parallel to the x-axis y x What do these coordinate pairs have in common? (0, 1), (4, 1), (–2, 1), (2, 1), (1, 1) and (–3, 1)? The y-coordinate in each pair is equal to 1. Look what happens when these points are plotted on a graph. All of the points lie on a straight line parallel to the x-axis. y = 1 Name five other points that will lie on this line. This line is called y = 1.

  6. Graphs parallel to the x-axis y x All graphs of the form y = c, where c is any number, will be parallel to the x-axis and will cut the y-axis at the point (0, c). y = 5 y = 3 y = –2 y = –5

  7. Drawing graphs of functions x –3 –2 –1 0 1 2 3 y = x – 2 For example, to draw a graph of y = x– 2: y = x - 2 1) Complete a table of values: –5 –4 –3 –2 –1 0 1 2) Plot the points on a coordinate grid. 3) Draw a line through the points. 4) Label the line. 5) Check that other points on the line fit the rule.

  8. Plot the following graphs y = 2x + 1 y = 2x +3 y = 2x y = 2x – 4 On the same axis in different colours

  9. Y = 2x + 3 Y = 2x + 1 Y = 2x Y = 2x - 4

  10. Drawing graphs of functions

  11. The equation of a straight line y = mx + c The general equation of a straight line can be written as: The value of m tells us the gradient of the line. The value of c tells us where the line crosses the y-axis. This is called the y-interceptand it has the coordinate (0, c). For example, the line y = 3x + 4 has a gradient of 3 and crosses the y-axis at the point (0, 4).

  12. Linear graphswith positive gradients

  13. A graph can have either a positive or a negative gradient

  14. 4 3 2 1 0 –4 –3 –2 –1 1 2 3 4 –1 –2 –3 –4 Working out the equation the straight line graph

  15. Exploring gradients

  16. 4 3 2 1 0 –4 –3 –2 –1 1 2 3 4 –1 –2 –3 –4 Working out the equation of the straight line graph

  17. 4 3 2 1 0 –4 –3 –2 –1 1 2 3 4 –1 –2 –3 –4 The equation of a straight line • Write down the equation of the straight line which has a gradient of –7 and cuts the y axis at the point (0, 4). Page 268

  18. Drawing graphs by rearranging equations

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