Study Notes
Graphs in algebra involve plotting linear equations on a Cartesian plane to visualize relationships between variables. Linear Function — a function that creates a straight line when graphed. Example: y = 2x + 3. 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 factors. Example: y in y = -2x + 3. Slope — the measure of the steepness of a line, denoted by m. Example: In y = 3x + 2, the slope is 3.
Exam Tips
Key Definitions to Remember
- Linear Function: A function that graphs to a straight line.
- Independent Variable: A variable that is not affected by other variables.
- Dependent Variable: A variable that depends on the independent variable.
- Slope: The steepness of a line on a graph.
Common Confusions
- Confusing the independent variable with the dependent variable.
- Forgetting to add arrows to indicate the line extends indefinitely.
Typical Exam Questions
- How do you graph the equation y = 2x + 3? Choose x-values, calculate y-values, plot points, and draw a line.
- What is the slope of the line y = -2x + 3? The slope is -2.
- How do you find where two lines intersect? Plot both lines and identify the crossing point.
What Examiners Usually Test
- Ability to plot linear equations accurately.
- Understanding of independent and dependent variables.
- Calculation and interpretation of the slope.