4.2 Coordinates and graphs

• The Cartesian plane
• Points on the Cartesian plane
• Table of values for a linear equation
• Scale for a linear equation
• Linear graphs
• Simultaneous linear equations

• draw a labelled Cartesian plane on different learning materials
• identify points on the Cartesian plane in different situations
• plot points on the Cartesian plane in different situations
• generate a table of values for a linear equation in different situations
• determine an appropriate scale for a linear equation on the Cartesian plane
• draw a linear graph from a table of values on the Cartesian plane
• solve simultaneous linear equations graphically in different situations
• apply simultaneous equations in real-life situations
• use IT or other resources to learn more on coordinates and graphs
• reflect on the use of graphs in real life

“How do we plot coordinates on a Cartesian plane?”

“Where do we use linear graphs in real life?”

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1. The Cartesian plane
   40 min · 1 practice tasks · quiz
   Drawing and labelling a pair of axes, naming the origin, and knowing what the grid is for.
2. Reading coordinates
   40 min · 1 practice tasks · quiz
   Finding the address of a point already marked on the plane, and writing it in the right order.
3. Plotting points
   40 min · 1 practice tasks · quiz
   Going the other way: given the coordinates, find the point and mark it accurately.
4. The four quadrants
   40 min · 1 practice tasks · quiz
   How the axes cut the plane into four regions, the sign pattern in each, and what happens on the axes themselves.
5. Choosing a scale
   40 min · 1 practice tasks · quiz
   Deciding how much one square is worth so that all the data fits on the paper and stays easy to read.
6. A table of values
   40 min · 1 practice tasks · quiz
   Turning a linear equation into a list of points by substituting one x value at a time.
7. Drawing a linear graph
   40 min · 1 practice tasks · quiz
   Taking a table of values through to a finished, labelled straight-line graph.
8. What the numbers in the equation do
   40 min · 1 practice tasks · quiz
   How the multiplier of x changes the steepness and the added number shifts the line up or down.
9. Reading answers off a graph
   40 min · 1 practice tasks · quiz
   Using a finished linear graph to answer questions in both directions, with a real charging example.
10. Two lines on one grid
    40 min · 1 practice tasks · quiz
    What happens when two linear graphs are drawn together, and what their crossing point means.
11. Solving simultaneous equations graphically
    40 min · 1 practice tasks · quiz
    Drawing two lines from two tables and reading the pair of values that satisfies both equations.
12. Forming equations from a story
    40 min · 1 practice tasks · quiz
    Turning two sentences of a word problem into two equations, starting by saying what the letters mean.
13. Simultaneous equations in real life
    40 min · 1 practice tasks · quiz
    Carrying a word problem all the way through: two equations, two lines, one crossing point, one sentence of answer.
14. Graphs in real life
    40 min · 1 practice tasks · quiz
    Reading travel graphs, trend graphs and comparison graphs, and saying what each shape means.