ILLUSTRATING A LINEAR FUNCTION || GRADE 8 MATHEMATICS Q2

Summary

This video explains the concept of linear functions, covering their definition, characteristics, and how to identify them through equations, tables, and graphs. It details the slope-intercept form (y = mx + b), where 'm' represents the slope and 'b' the y-intercept. The video demonstrates how to determine if a function is linear by examining its equation or the table of values. It also highlights the difference between linear and non-linear relationships with practical examples, such as comparing the perimeter and area of a square. Overall, it provides an accessible introduction to linear functions in algebra.

Takeaways

• 😀 A linear function is a mathematical function that can be written in the form f(x) = mx + b, where m is the slope and b is the y-intercept.
• 😀 The graph of a linear function is always a straight line, and the function itself represents a constant rate of change between the independent and dependent variables.
• 😀 In the slope-intercept form f(x) = mx + b, m represents the slope, which tells how steep the line is, and b represents the y-intercept, which is the point where the graph crosses the y-axis.
• 😀 The equation y = mx + b is equivalent to f(x) = mx + b, meaning y can be used in place of f(x).
• 😀 Linear functions are not only expressed using f(x); other notations like g(x) and h(x) can also be used to represent them.
• 😀 To identify a linear function, the equation should be in the form y = mx + b, and both x and y should have a degree of 1. If there is an exponent greater than 1, the function is not linear.
• 😀 Non-linear equations include those where variables are in the denominator or the highest degree of a variable is greater than 1, such as x^2 or 1/x.
• 😀 A table of values is linear if the dependent variable (y) increases or decreases by a constant amount as the independent variable (x) changes by a consistent amount.
• 😀 For example, if the perimeter of a square increases by 4 units for each 1-unit increase in the side length, it represents a linear function.
• 😀 In contrast, the area of a square does not form a linear function because the change in the area is not constant as the side length increases.
• 😀 The equation of a linear function can be graphed as a straight line, and the graph will reflect the slope and y-intercept of the equation.

Q & A

What is a linear function?

A linear function is a function that can be written in the form f(x) = mx + b, where m is the slope of the line, and b is the y-intercept. The graph of a linear function is always a straight line.

What does the 'm' in the linear function equation represent?

In the equation f(x) = mx + b, the 'm' represents the slope of the line, which indicates how steep the line is. It shows the rate of change in y with respect to x.

What does the 'b' in the linear function equation represent?

In the equation f(x) = mx + b, the 'b' represents the y-intercept, which is the point where the graph of the function crosses the y-axis.

Is y = 3x + 4 a linear function?

Yes, y = 3x + 4 is a linear function because it is in the form y = mx + b, with m = 3 and b = 4.

Why is y = x^2 not a linear function?

y = x^2 is not a linear function because it does not form a straight line. It is a quadratic function where the highest degree of x is 2.

How can you tell if a function represented by a table is linear?

To determine if a function is linear from a table, check if the change in the y-values is constant when the x-values increase by the same amount. If the change is not constant, the function is not linear.

What is the relationship between the side of a square and its perimeter in terms of linearity?

The relationship between the side of a square and its perimeter is linear. As the side length increases by one unit, the perimeter increases by a constant value of 4.

Why is the relationship between the side of a square and its area not linear?

The relationship between the side of a square and its area is not linear because the area increases by non-constant amounts as the side length increases. The area follows a quadratic pattern.

What is the difference between linear and non-linear functions when graphed?

The graph of a linear function is always a straight line, while the graph of a non-linear function is not a straight line. Non-linear functions may curve or change direction.

In the equation y = 4x, what is the value of the slope?

In the equation y = 4x, the slope is 4. This means that for every 1 unit increase in x, y increases by 4 units.