Welcome to 8th grade algebra! Algebra is a fundamental branch of mathematics that uses letters and symbols to represent numbers and quantities. Instead of working with specific numbers, we use variables like x and y to create general formulas and equations. This allows us to solve problems and find patterns that work for many different situations.
In algebra, variables are symbols like x, y, a, and b that represent unknown numbers. Think of them as placeholders that can hold different values. We combine these variables with numbers and mathematical operations like addition, subtraction, multiplication, and division to create algebraic expressions. For example, three x plus five, or two y minus seven.
Linear equations contain variables raised only to the first power. To solve them, we use inverse operations to isolate the variable. Let's solve two x plus three equals eleven. First, we subtract three from both sides to get two x equals eight. Then we divide both sides by two to get x equals four. Think of it like a balance scale - whatever we do to one side, we must do to the other.
When we graph linear equations, they always form straight lines. The equation y equals m x plus b is called slope-intercept form. The slope m tells us how steep the line is - it's the rise over run. The y-intercept b shows where the line crosses the y-axis. Let's look at three examples with different slopes and y-intercepts.