Hong Kong
Stage 4 - Stage 5

# Linear modelling

Lesson

Now that we know how:

• to graph linear relationships
• to find the equations of linear functions
• to use algebra and graphs to extract information and
• the gradient of a linear function represents constant change,

we can put this to use to solve a range of real life applications.

It's all the same mathematics, but this time you will have a context to put upon it.

We can also use graphs to determine information about these kinds of linear relationships.

Some examples will be the best way to show you how the mathematics we have learnt can be applied to everyday situations.

#### Worked Examples

##### Question 2

The graph shows the price charged by a medical specialist for a consultation.

1. How much does it cost for an adult whose consultation takes $9$9 minutes?

2. How much does it cost for a student whose consultation takes $9$9 minutes?

3. What is the hourly rate for an adult?
4. What is the hourly rate for a student?
5. What is the percentage discount for a student?

##### Question 3

The travel graph of John and Kate is shown.

1. How many more hours did John take to travel than Kate?

2. What is John's average speed in km/h for the trip?

3. What is Kate's average speed in km/h for the trip?

4. At what time did the distance travelled by Kate equal the distance travelled by John?

$12$12 pm

A

$11:15$11:15 am

B

$11:30$11:30 am

C

$10:30$10:30 am

D
5. At the time when Kate and John had travelled equal distances, what was the actual distance travelled?

##### Question 4

Deborah left for a road trip at midday. The following graph shows the total distance travelled (in kilometres) $t$t hours after midday.

1. Find the gradient of the straight line.

2. What does the gradient of the line represent?

the total distance travelled

A

the car’s speed

B

the car's acceleration

C