Lesson Notes By Weeks and Term v5 - Grade 9
Functions and graphs (linear and simple non-linear) – Week 10 focus
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Functions and graphs (linear and simple non-linear) – Week 10 focus
Download the Lessonotes Mobile South Africa app for faster lesson access on Android and iPhone.
Subject: Mathematics
Class: Grade 9
Term: 2nd Term
Week: 10
Theme: General lesson support
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Functions and graphs are fundamental building blocks in mathematics. Understanding them unlocks the ability to model real-world relationships and make predictions. For a South African learner, this means understanding how mobile data costs vary with usage, how income relates to hours worked at a part-time job, or even how the price of a bunny chow might change based on ingredient costs. Without understanding functions, we are simply accepting numbers without understanding the relationships between them. This week, we will specifically focus on linear functions and simple non-linear functions, such as quadratics, and their graphical representation.
Linear Functions: y = mx + c A linear function is a function that forms a straight line when graphed.
It's written in the form: y = mx + c y: The dependent variable (output). x: The independent variable (input). m: The gradient (slope) of the line. It represents the rate of change of y with respect to x. A positive gradient means the line slopes upwards from left to right; a negative gradient means it slopes downwards. The steeper the line, the larger the absolute value of m. c: The y-intercept. This is the point where the line crosses the y-axis (where x = 0).
Understanding the Gradient (m): The gradient 'm' can be calculated using two points on the line, (x₁, y₁) and (x₂, y₂): m = (y₂ - y₁) / (x₂ - x₁) The gradient tells us how much 'y' changes for every one unit change in 'x'. For instance, if m = 2, for every 1 unit you move to the right on the x-axis, you move 2 units up on the y-axis.