Linear Equations

Linear equations are those which make straight lines when graphed.

Real life examples include:

• Calculating wages based on an hourly pay rate
• Calculating medicine doses based on patients' weights
• Calculating the perimeters of squares
• Hiring a car if a deposit is paid and there is an hourly charge

Algebraic examples include:

• y = 3x + 4
• y = 2x
• 4x + 5y – 2 = 0

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.

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

(b)

 Number of hours worked, x 0 1 2 Pay (\$), y 0 10 20 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.

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

(b)

 Mass (kg), x 10 20 30 Dose (millilitres), y 50 100 150 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.

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

(b)

 Number of hours hired, x 0 1 2 Cost (\$), y 50 70 90 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.