1. Linear Equations & Graphing
Math 8

2. Key Words & Definitions
Distributive Property – the property stating that a product can be written as a sum or a different of two products.
Example: a(b + c) = ab + ac
a(b – c) = ab - ac
Expand – to distribute numbers or variables in an equation, allowing us to perform simplified operations (such as multiplication, subtraction, etc…)

3. Key Words & Definitions
Linear Relation – a relation that has a straight line graph.
Example: a simple input/output table
The input is the number we substitute in for the variable
The output is the number we calculate using the variable
Draw it or use next slide.

4. Linear Relation

5. Key Words & Definitions
Ordered Pair – two numbers in order, for example (2, 4); on a coordinate grid, the first number is the horizontal coordinate of a point and the second number is the vertical coordinate of the point. (x,y)
Example: look at the previous input/output table. Every set of input & output gives us an ordered pair.
(1, 17), (2, 14), (3, 11), (4, 8), etc.
Discrete Data – data that can be counted.

6. Learning Intentions Graph & analyze two variable linear relations
Solve linear equations
Concretely
Pictorially
symbolically
Solve algebraic word problems

7. Solving Equations Using Algebra
It can be inconvenient to model an equation using algebra tiles when large numbers are involved or when the solution is a fraction or a decimal.
Let’s look at some basic steps for solving problems!

8. Solving Equations Using Algebra
16t – 69 = t – = t = 56 16t/16 = 56/16
First: Isolate the variable term.
Second: Solve for the variable.
Third: Divide & simplify.
Finish problem as a fraction and a calculator

9. Remember! Positive x positive = positive
Positive x negative = negative
Negative x positive = negative
Negative x negative = positive
Positive ÷ positive = positive
Negative ÷ negative = positive
Positive ÷ negative = negative
Negative ÷ positive = negative

10. Practice
Do questions:
5. a,c,e,f
6. a,b,c,d
8. a,b,c,d
9. a,b,c

11. More practice

12. Supplemental Workbook
Work on pages