215. Linear Parameters

Learning Intentions

• Identify parameters in linear functions.
• Describe how gradient changes the steepness of a line.
• Explain how the y-intercept shifts a Draw vertically.

Pre-requisite Summary

• Understand linear functions in the form .
• Plot points using coordinates .
• Recognise gradient as rate of change.
• Identify the y-intercept as where .
• Substitute values into linear equations.

Worked Examples

Worked Example 1

Identify the parameters in the linear function:

State:

• Gradient
• y-intercept

Worked Example 2

Compare steepness of:

and

Worked Example 3

Explain the transformation from:

to

Problems

Problem 1

Identify gradient and y-intercept:

Problem 2

Compare steepness:

and

Problem 3

Describe the transformation:

Exercises

Understanding and Fluency

Exercise 1

Identify gradient and y-intercept:

Exercise 2

Identify gradient and y-intercept:

Exercise 3

State whether increasing or decreasing:

Exercise 4

Compare steepness:

Exercise 5

Compare steepness:

Exercise 6

Describe the effect:

Exercise 7

Identify parameters:

Exercise 8

State y-intercept:

Exercise 9

State gradient:

Exercise 10

Describe change from to

Exercise 11

Explain why gradient controls steepness.

Exercise 12

Explain why y-intercept does not affect steepness.

Exercise 13

Correct the misconception:

“If y-intercept increases, the line gets steeper.”

Exercise 14

State what stays the same when only gradient changes.

Exercise 15

Interpret:

Exercise 16

Compare:

A:

B:

Exercise 17

Describe transformation:

Potential Misunderstandings

• Confusing gradient with y-intercept
• Thinking y-intercept changes steepness
• Misidentifying and
• Assuming negative gradients are incorrect rather than decreasing
• Forgetting vertical shift only affects position
• Mixing x-intercept and y-intercept
• Believing steepness depends on graph position

Next: 216. Quadratic Parameters