Study Notes
Graphs in algebra involve plotting linear functions on a Cartesian plane. Linear Function — a function that creates a straight line when graphed. Example: y = 3x + 2. Independent Variable — a variable that determines the value of another variable. Example: x in y = -2x + 3. Dependent Variable — a variable whose value depends on another variable. Example: y in y = -2x + 3. Slope — the measure of the steepness of a line, calculated as rise over run. Example: For points (1,2) and (3,4), slope m = (4-2)/(3-1) = 1.
Exam Tips
Key Definitions to Remember
- Linear Function: A function that graphs to a straight line.
- Independent Variable: A variable that influences another variable.
- Dependent Variable: A variable influenced by another variable.
- Slope: The steepness of a line, rise over run.
Common Confusions
- Mixing up independent and dependent variables.
- Forgetting to add arrows on the graph to show it extends indefinitely.
Typical Exam Questions
- How do you find the slope between two points? Subtract the y-values and divide by the difference in x-values.
- What does the intersection of two lines represent? The solution to the simultaneous equations.
- How do you plot a linear equation? Choose x-values, find corresponding y-values, plot points, and draw a line.
What Examiners Usually Test
- Ability to plot linear graphs accurately.
- Understanding of slope and its calculation.
- Solving simultaneous equations graphically.