# 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.

**Answer:**

(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.

**Answer:**

(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.

**Answer:**

(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.

**Answers**

**A1.** y = 2x

**A2.** y = 4x

**A3.** y = 200x + 1000