Linear Equations & Graphing Math 8

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…)

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.

Linear Relation

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.

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

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!

Solving Equations Using Algebra 16t – 69 = -13 16t – 69 + 69 = -13 + 69 16t = 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

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

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

More practice

Supplemental Workbook Work on pages 142-143