Learn to identify patterns and write linear equations. Grade 9 Alberta mathematics curriculum.
Lesson 4.1 of Linear Equations in Grade 9 Math — Alberta curriculum lessons.
🔵 Independent Variable. A variable whose value is not determined by the other variable. It does not depend on anything.
Example. If you're earning money by working hours: the number of hours worked is the independent variable because you can choose how many hours to work — it doesn't depend on anything else.
🔴 Dependent Variable. A variable whose value is determined by the other variable. It always depends on the independent variable.
Example. If you're earning money by working hours: the amount of money earned is the dependent variable because it depends on how many hours you work. More hours = more money!
💡 Remember. The dependent variable depends on the independent variable.
💡 Expression. An expression is a mathematical statement made up of numbers and/or variables connected by operations.
Important!. An expression does NOT contain an equal sign!
💡 Equation. An equation is a mathematical statement where two expressions are equal.
Important!. An equation must have an equal sign!
The Difference. Think of it this way:
🚗 Lucas's Driveway Shoveling Business. Lucas decides to shovel driveways this winter to earn money. He charges 9 per hour for his work.
We have two quantities changing:
🔵 Independent Variable. Hours worked: this is the independent variable (x)
🔴 Dependent Variable. Money earned: this is the dependent variable (y)
Key Insight. The money depends on the number of hours. If hours change, the money changes too.
🟢 Pattern. Each time x increases by 1, y increases by 9.
Look at how y changes when x increases by 1.
🔍 Observation. When hours go up by 1, money goes up by 9.
🟢 Rate of Change. That's our rate of change (sometimes called the slope). It tells us how much y changes for each x.
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