Functions, Graphs and Equations

Horizontal and Vertical Straight Line Graphs

Plotting Graphs on a Grid

Using Graphs to Solve Linear Equations

Interpreting Linear Graphs

Using Real Life Graphs

Drawing Parabolas

Using Parabolas to Solve Quadratic Equations

Prerequisite Knowledge

• Use coordinates in all four quadrants
• Substitute positive and negative numbers into formulae
• Solve a two-step linear equation
• Simplify an expression by collecting like terms.
• Expand and factorise algebraic expressions

Key Concepts

• Graphs are used to show a relatioship between x and y values.  This relationship can be written as an equation.
• A straight line graph is made up of a gradient, denoted as M which determines the steepness and an intercept, denoted as C, which determines where the line crosses the y axis.
• A graph is a visual representation of a continuous function.  Students often mistakenly draw line segments at the two extreme x values.
• It can be helpful to record x and y values in a table when calculating the coordinates for any graph.
• Quadratic graphs are in the shape of a parabola and symmetrical about the turning point.
• When using a graph to solve an equation the solution can be taken as an estimate due to the inaccuracies of measurements and drawings.
• Graphs can be used to model situations as the line represents a continuous set of results.

Working mathematically

Develop fluency

• Move freely between different numerical, algebraic, graphical and diagrammatic representations [for example, equivalent fractions, fractions and decimals, and equations and graphs]
• Develop algebraic and graphical fluency, including understanding linear and simple quadratic functions

Reason mathematically

• Identify variables and express relations between variables algebraically and graphically

Solve problems

• Begin to model situations mathematically and express the results using a range of formal mathematical representations
• Select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems.

Functions, Graphs and Equations Subject Content

Algebra

• Work with coordinates in all four quadrants
• Recognise, sketch and produce graphs of linear and quadratic functions of one variable with appropriate scaling, using equations in x and y and the Cartesian plane
• Interpret mathematical relationships both algebraically and graphically
• Reduce a given linear equation in two variables to the standard form y = mx + c; calculate and interpret gradients and intercepts of graphs of such linear equations numerically, graphically and algebraically
• Use linear and quadratic graphs to estimate values of y for given values of x and vice versa and to find approximate solutions of simultaneous linear equations
• Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs