Summary
Graphs in algebra involve plotting linear equations on a Cartesian plane to visualize relationships between variables. Linear Function — a function that graphs to a straight line. Example: y = 3x + 2. Independent Variable — a variable that stands alone and isn't changed by other variables. Example: x in y = -2x + 3. Dependent Variable — a variable that depends on other variables. Example: y in y = -2x + 3. Slope — the measure of the steepness of a line, calculated as rise over run. Example: m in y = mx + c.
Exam Tips
Key Definitions to Remember
- Linear Function: A function that graphs to a straight line.
- Independent Variable: A variable that stands alone and isn't changed by other variables.
- Dependent Variable: A variable that depends on other variables.
- Slope: The measure of the steepness of a line, calculated as rise over run.
Common Confusions
- Mixing up independent and dependent variables.
- Forgetting to add arrows on the ends of the graph line to show it extends indefinitely.
Typical Exam Questions
- How do you graph the equation y = 3x + 2? Choose x-values, find corresponding y-values, plot points, and draw a line.
- What is the slope of the line passing through points (1, 2) and (3, 6)? Slope is (6-2)/(3-1) = 2.
- What does the intersection of two lines on a graph indicate? The solution to the simultaneous equations.
What Examiners Usually Test
- Ability to plot linear graphs accurately.
- Understanding of the relationship between independent and dependent variables.
- Calculation and interpretation of the slope.