• Mathematics
• Year 9

# Linear Relationships

approx. 10 hrs

6 topics

22 concepts

Master Linear Relationships and establish the right foundations for Year 10

Available in
ACT NSW NT QLD SA TAS VIC WA

### Overview

Linear Relationships investigates the relationship between two variables by examining the algebraic and graphical form of a straight line. In this learning program, students calculate the gradient of a line and evaluate the impact of its value on the algebraic and graphical form of a linear relationship. Students draw a linear relationship on the Cartesian plane using a table of values and communicate the similarities and differences between two or more straight lines.

### Topics & Concepts We Cover

This learning program is made up of the following 6 topics, broken down into 22 concepts.

• #### Interpret and Graph Straight Lines 6 concepts

1. Sketch a linear graph using the coordinates of two points i.e. x and y-intercepts if possible

2. Form of a vertical line including the equation of the y-axis

3. Form of a horizontal line including the equation of the x-axis

4. Finding the x - intercept at y=0

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

6. Finding the y - intercept at x=0

• #### Gradient of a Line 5 concepts

1. Connection between gradient, rate problems and direct proportion

2. Classify the nature of a gradient from a linear function

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

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

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

• #### Determine Equation of a Line 5 concepts

1. Match a linear graph with its equation

2. Determine whether a point lies on a line by substitution

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

4. Finding the equation of a line given a point and the gradient

5. Reading the x and y intercept from a graph

• #### Midpoint and Length of an Interval 2 concepts

1. Calculating the 'mean' to find the midpoint, M, of the interval

2. Using Pythagoras' theorem to calculate distance between two points

• #### Parallel and Perpendicular Lines 2 concepts

1. Apply the property that perpendicular lines have gradients that are negative reciprocals of each other

2. Apply the property that parallel lines have equal gradients

• #### Apply Linear Relationships 2 concepts

1. Solve practical problems involving linear relationships

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

### 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 Relationships

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