Equations of Straight Line Graphs

Plotting Straight Line Graphs y = mx + c

Straight Line Graphs in the Form ax + by = c

Finding the Gradient of Straight Lines

Gradient of Parallel Lines

Deriving the Equation of a Straight Line

Gradient of Perpendicular Lines

Equation of Straight Line Graphs

Prerequisite Knowledge

• 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

• 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.
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• 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.