Direct Variation

Review​

Addition, subtraction, multiplication and division of radicals​

Draw

Simplify $$\left(\sqrt[]{7}\right)^2$$  

Draw

Perform the operation and simpify. $$\left(\sqrt[]{2}\right)^{ }\left(\sqrt[]{5}\right)^{ }$$  

Draw

Multiply $$\sqrt[]{3}^{ }\left(5-4\sqrt[]{2}\right)^{ }$$  

​At the end of the lesson, you will be able to;

​a) solve equations involving radical expressions

​b) illustrate direct variation and direct square variation

Draw

Given $$\sqrt[]{y}=7$$  What is the result when we square both sides?

Open Ended

Describe what happens to the radical symbol? $$\sqrt[]{y}=7\ becomes\ y=49$$  

Multiple Choice

What laws of radical supports your answer?

• $$Law\ 1.\ \sqrt[x]{x^n}=\ x$$  

• $$Law\ 2.\ \sqrt[n]{xy}=\sqrt[n]{x}\cdot\sqrt[n]{y}$$  

• $$Law\ 3.\ \sqrt[n]{\frac{x}{y}}=\frac{\sqrt[n]{x}}{\sqrt[n]{y}}$$  

Draw

What value of y satisfies the equation? $$\sqrt[]{y}=7$$  

​Equations and Problems Involving Radicals

​See example 1 and 2 on page 205

Open Ended

Why is it necessary to check if the value that you have solve is really a solutionn to the given equation?

Direct Variation​

Examples 1 and 2 on page 136-137​

Multiple Choice

Examine the table, what can you observe?

• As the time increases, the distance decreases

• As the time increases, the distance increases

• As the time increases, the distance is constant

• As the time decreases, the distance decreases

Multiple Choice

Complete the table with the correct value.

• 145

• 140

• 135

Open Ended

Name one most important attributes of a student that vary directly with his or her academic performance.

​Inverse Variation

See example found on page 141​

Multiple Choice

The graph shows the number of hours y that a loaders (x) can fill a truck. How many hours can 4 loaders fill a truck?

• 4

• 2

• 1

Multiple Choice

What equation relates the number of hours required to fill a truck and the number of loaders used?

• $$y=4x$$  

• $$y=\frac{x}{4}$$  

• $$y=\frac{4}{x}$$