AeroLab Reading room

MATH / Foundations

Patterns, variables and graphs

A variable stands for a quantity that may change. An expression describes a calculation; an equation asserts that two expressions have the same value.

Learning objectives

The big idea

A variable stands for a quantity that may change. An expression describes a calculation; an equation asserts that two expressions have the same value.

A graph pairs inputs with outputs. Label axes and scales so a point has an unambiguous meaning; a pattern seen in a few points is evidence, not a proof for every input.

Equations and relationships

y=mx+cy=mx+c

m is the gradient and c is the vertical intercept of a straight line.

Worked example

If y = 2x + 3, find y when x = 4.

Follow the solution

Substitute x = 4: y = 2 × 4 + 3 = 11.

Investigate and explain

Predict the worked result before calculating. Change one input, record the new result, and explain which assumptions still hold.

Related interactive model. Compare its assumptions with the explanation; it is not a complete syllabus lesson.

Open the interactive investigation

Check your understanding

1. Which operation keeps an equation balanced?

  1. Add the same number to both sides
  2. Add only to the left side
  3. Square only the right side
Check the answer and reasoning

Add the same number to both sides

Equal operations on equal quantities preserve equality when defined.

2. If y = 2x + 3, find y when x = 4.

  1. 14
  2. 11
  3. 9
Check the answer and reasoning

11

Substitute x = 4: y = 2 × 4 + 3 = 11.

3. For y = 2x + 3, how much does y rise when x rises by 1?

  1. 3
  2. 5
  3. 2
Check the answer and reasoning

2

The coefficient of x gives a constant rise of 2 for each unit increase.