# Linear Graphs

Students learn how to create a table of results to  plot and recognise the features of a straight line graph in the form y = mx + c.  As learning progresses they use graphs to model and solve equations.

This unit takes place in Term 5 of Year 10 and is followed by graphical functions.

##### Prerequisite Knowledge
• Describe positions on a 2-D grid as coordinates in the first quadrant
• Describe positions on the full coordinate grid (all four quadrants)
• Recognise and describe linear number sequences, including those involving fractions and decimals, and find the term-to-term rule.
• Generate and describe linear number sequences
##### Success Criteria
• Interpret simple expressions as functions with inputs and outputs;
• Work with coordinates in all four quadrants
• Plot graphs of equations that correspond to straight-line graphs in the coordinate plane;
• Use the form y = mx + c to identify parallel lines
• Find the equation of the line through two given points, or through one point with a given gradient
• Identify and interpret gradients and intercepts of linear functions graphically and algebraically
##### Key Concepts
• Gradient is a measure of rate of vertical change divided by horizontal change.
• Parallel lines have the same gradient
• The intercept always has the x value equal zero.
##### Common Misconceptions
• Students often confuse linear graphs to have the same notation as statistical graphs.
• The gradient can be calculated from any two points along the graph. Not necessarily from the origin.
• A linear function does not have to pass through the origin.
• It is beneficial to create a table of results when plotting a linear function. The coordinate pairs arise from the x and y values.

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