Lesson Notes By Weeks and Term v4 - SHS 1
PATTERNS AND RELATIONS
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PATTERNS AND RELATIONS
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Subject: Mathematics
Class: SHS 1
Term: 1st Term
Week: 16
Grade code: 1.2.2.LI.2
Strand code: 2
Sub-strand code: 2
Content standard code: 1.2.2.CS.1
Indicator code: 1.2.2.LI.2
Theme: ALGEBRAIC REASONING
Subtheme: PATTERNS AND RELATIONS
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This lesson introduces students to the concept of linear functions and their graphical representation. In our daily lives in Ghana, we encounter many situations where one quantity changes at a constant rate in relation to another. For example, the cost of buying multiple balls of kenkey, the total fare for a "tro-tro" journey based on distance, or the amount of mobile data consumed over time. Understanding linear graphs helps us to model, visualise, and make predictions about these real-world relationships. This lesson will equip learners with the skills to draw these graphs and, more importantly, understand what they tell us.
Concept 1: What is a Linear Function?
A linear function is a relationship between two variables (usually `x` and `y`) that, when plotted on a graph, produces a straight line. The key feature is that the highest power of the variable `x` is 1.
There are two common forms of a linear equation: Slope-Intercept Form: `y = mx + c` `m` is the gradient (or slope) of the line. It tells us how steep the line is and in which direction it goes. A positive gradient means the line slopes upwards from left to right. A negative gradient means it slopes downwards. `c` is the y-intercept. This is the point where the line crosses the vertical y-axis. Its coordinate is always `(0, c)`. General Form: `ax + by + c = 0` Here, `a`, `b`, and `c` are constants. This form can always be rearranged to the slope-intercept form (`y = mx + c`) to easily identify the gradient and y-intercept.
Example 1: Identifying a Linear Equation A teacher asks you if the equation `5x - 2y = 10` will form a straight line graph. How would you know without plotting it?