Linear Equations

Linear equations are those which make straight lines when graphed.

Real life examples include:

Algebraic examples include:


Example One - Calculating Wages

Jack earns $10 per hour. How much does he earn for working up to 2 hours?

(a) Write the linear equation.
(b) Draw a table and a graph showing his wages.

Answer:
(a) Let x = the number of hours worked and y = wages
The equation is y = 10x

(b)

Number of hours worked, x012
Pay ($), y01020

Calculating Wages diagram


Example Two - Medicine Doses

Medicine doses are calculated on people's masses. A small child will receive less than a heavier adult.
For a particular medicine the dosage for a 10kg child is 50 millilitres.

(a) Write the equation.
(b) Draw a table and a graph for the dosages for people up to 30kg.

Answer:
(a) Let x = the patient's mass and y = medicine dose
The equation is y = 5x

(b)

Mass (kg), x102030
Dose (millilitres), y50100150

Medicine Dosage diagram


Example Three - Car Hire Cost

Car hire cost includes a deposit of $50 plus an hourly rate of $20. How much does it cost to hire the car for up to 2 hours?

(a) Write the equation.
(b) Draw a table and a graph.

Answer:
(a) Let x = the number of hours and y = total hire cost
The equation is y = 20x + 50

(b)

Number of hours hired, x012
Cost ($), y507090

Car Hire diagram

Questions

Write the linear equations for the following situations:
Q1. I pay $2 for every movie I hire.
Q2. The number of legs of goats in a paddock.
Q3. The hire costs of a yacht with a deposit of $1000 plus a daily charge of $200.

Answers
A1. y = 2x
A2. y = 4x
A3. y = 200x + 1000