• Mathematics General
• Year 11

# Linear equations and their graphs

approx. 10 hrs

6 topics

33 concepts

Build mastery in modelling and analysing linear relationships in practical contexts.

Available in
ACT NT QLD SA TAS WA

### Overview

Linear equations and their graphs uses linear equations and straight-line graphs to model and analyse the relationship between two variables. The scope of this program includes piecewise-linear and step graphs as well as the graphical representation of simultaneous linear equations to explore breakeven analysis.

### Topics & Concepts We Cover

This learning program is made up of the following 6 topics, broken down into 33 concepts.

• #### Solve literal equations 7 concepts

1. Use a CAS calculator to solve a literal equation

2. Solve equations with one algebraic fraction

3. Equations with pronumerals on both sides

4. Generate and solve linear equations from word problems and interpret the results

5. Solve three-step equations

6. Solve one-step equations

7. Solve two-step equations

• #### Straight-line graphs 11 concepts

1. Find the equation of a line from two points using a CAS calculator

2. Construct a linear graph and generate a table of values using a CAS calculator

3. Finding the x - intercept at y=0

4. Find the equation of a line given the gradient and the y-intercept

5. Find the gradient of a line between two points using formulae

6. Reading the x and y intercept from a graph

7. Sketch a linear relationship from a table of values on a cartesian plane

8. Determine the gradient and y-intercept using the gradient-intercept form of a linear relationship

9. Use the gradient and y-intercept to graph a linear equation

10. Find the gradient of a line between two points using rise over run

11. Finding the y - intercept at x=0

• #### Linear Modelling 3 concepts

1. Interpret linear models

2. Construct a linear model

3. Establish meaning for the gradient and intercepts in a practical context

• #### Solve equations simultaneously 7 concepts

1. Use a CAS calculator to find the point of intersection of two linear graphs

2. Solve simultaneous equations using a CAS calculator

3. Generate and solve linear simultaneous equations from word problems and interpret results

4. Solve linear simultaneous equations by finding the point of intersection of their graphs

5. Solve linear simultaneous equations using elimination method where one or both of the equations need to be modified

6. Solve linear simultaneous equations using substitution method

7. Solve linear simultaneous equations using elimination method

• #### Break-even analysis 1 concept

1. Apply break-even analysis to linear models

• #### Piecewise linear graphs and step graphs 4 concepts

1. Sketch a step graph

2. Sketch a piecewise linear graph

3. Analyse step graphs

4. Use a piecewise linear function to model and solve practical situations

### What you'll get

Learning Content

• A customised learning plan to suit your needs, adapting to your pace as you learn, progress and achieve mastery
• All the content required to help you master the syllabus, including theory, worked examples, exam preparation and practice questions

An Expert Tutor

• We match you to a private, expert tutor who is right for your needs and goals
• Our tutors are talented, tested, top ATAR achievers and subject experts
• During each session, your tutor guides you through your learning program, providing real-time, live expert tutoring in Linear equations and their graphs

Reporting

• Access information at every stage showing what's been mastered, what areas need to be worked on and what's next
• You and your parents receive a comprehensive feedback report after every session
• Every session is recorded and available for you to watch at any time, allowing you to review what was covered

### Ready to start this program?

Simply pick a time that works for you

We'll be in contact to match you with one of our top tutors and book your first session

Starting at

\$49(inc. GST)

per session

Fully flexible

PAYG and bundle plans

Use anytime