Linear Equations
In this chapter, you will solve equations using the balance method and determine the formula for linear graphs.
theory
Balance Method
Take a look at the equation: 2x - 6 = 8
This equation states that You can simplify the equation step by step, applying the same operation on both sides. This way the equation remains balanced, like a pair of weighing scales.
Add 6 to both sides | |
Divide both sides by 2 | |
Exercise 1
Solve these equations using the balance method.
a
b
c
practice
example
Writing linear functions
A new candle is 30 cm long. One burning hour reduces the height by 1.5 cm.
a
Write this as a mathematical function f(t)
, where t
is time in hours.
Solution: f(t) = 30 - 1.5 \cdot t
b
What is the height of the candle after 5 hours?
Solution: f(5) = 30 - 1.5 \cdot 5 = 30 - 7.5 = 22.5
cm
c
After how many hours has the candle burnt out?
Solution: Solve f(t)=0
:
(click on a step for details)
Exercise 2
Try to find the function values for the given