Linear Functions

Summary and Exam Tips for Linear Functions

Linear Functions is a subtopic of Algebra, which falls under the subject Mathematics in the IB MYP curriculum. In linear functions, the gradient and intercept are crucial components of the line equation. The gradient, or slope, represents the ratio of the change in $y$ coordinates to the change in $x$ coordinates, expressed as $\frac{\Delta y}{\Delta x}$. The intercept is the point where the line crosses the $y$-axis, indicating the starting value of $y$ when $x = 0$.

A line with a zero gradient is horizontal, while a vertical line's equation is undefined in terms of gradient. Parallel lines have identical gradients and never intersect, whereas perpendicular lines intersect at a right angle, with gradients that are negative reciprocals of each other. Understanding these concepts is essential for solving practice questions that involve determining gradients and identifying parallel or perpendicular lines.

Exam Tips

• Understand the Equation: Familiarize yourself with the line equation $y = mx + c$, where $m$ is the gradient and $c$ is the intercept.
• Calculate Gradients: Practice finding the gradient using coordinates with the formula $\frac{\Delta y}{\Delta x}$.
• Identify Line Relationships: Know how to determine if lines are parallel or perpendicular by comparing their gradients.
• Practice Questions: Regularly solve practice questions to reinforce your understanding of linear functions and their properties.
• Visualize Graphs: Sketch graphs to better understand the relationship between the gradient and intercept visually.