# Linear Graphs

Scheme of work: GCSE Foundation: Year 10: Term 5: Linear Graphs

#### 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

• The gradient measures the 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 with having 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.

## Linear Graphs Resources

### Mr Mathematics Blog

#### Estimating Solutions by Rounding to a Significant Figure

Explore key concepts, FAQs, and applications of estimating solutions for Key Stage 3, GCSE and IGCSE mathematics.

#### Understanding Equivalent Fractions

Explore key concepts, FAQs, and applications of equivalent fractions in Key Stage 3 mathematics.

#### Transforming Graphs Using Function Notation

Guide for teaching how to transform graphs using function notation for A-Level mathematics.