ILLUSTRATING LINEAR EQUATIONS IN TWO VARIABLES || GRADE 8 MATHEMATICS Q1

Summary

This video introduces linear equations in two variables, explaining the general and slope-intercept forms. It covers the structure of equations in the form of ax + by = c, where a, b, and c are real numbers, and how to identify the coefficients and constants. The video walks through creating a table of values for x and y, determining solutions, and testing whether given points are solutions. Additionally, it explains plotting these points on a graph, emphasizing that linear equations always produce straight lines. Examples and exercises help reinforce the key concepts.

Takeaways

• 📘 Linear equations in two variables can be written in the form ax + by = c, where a, b, and c are real numbers, and neither a nor b can be zero.
• 📝 The coefficients in the general form of the equation ax + by = c are a and b, while c is the constant.
• ⚙️ The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
• 🎯 Linear equations must have two variables (x and y) and be of the first degree (the exponent of the variables should be 1).
• 📉 To solve for y in terms of x, rearrange the general form into the slope-intercept form y = mx + b.
• 🧮 Examples of linear equations in two variables include x + y = 4, 2x = 4y - 2, and 12 = 2x + 3y.
• ❌ Equations like x² - 3y = -5 are not linear equations in two variables because the degree of x is greater than 1, making it quadratic.
• 📊 A table of values can be constructed to find ordered pairs (x, y) that satisfy a given linear equation, allowing the equation to be graphed.
• 📏 The graph of any linear equation is always a straight line, with infinitely many solutions that satisfy the equation.
• 🔍 To check if an ordered pair is a solution, substitute the values of x and y into the equation to see if they satisfy the equation.

Q & A

What is a linear equation in two variables?

A linear equation in two variables is an equation that can be written in the form ax + by = c, where a, b, and c are real numbers, and a and b are not equal to zero.

What are the coefficients in the linear equation ax + by = c?

In the linear equation ax + by = c, a and b are the coefficients of the variables x and y, respectively.

What is the constant in the linear equation ax + by = c?

The constant in the linear equation ax + by = c is represented by c.

What is the slope-intercept form of a linear equation and what does 'm' represent?

The slope-intercept form of a linear equation is y = mx + b, where 'm' represents the slope of the line.

What is the y-intercept in the slope-intercept form y = mx + b?

In the slope-intercept form y = mx + b, 'b' represents the y-intercept, which is the point where the line crosses the y-axis.

How can you determine if a given equation is a linear equation in two variables?

An equation is a linear equation in two variables if it has two variables, both to the first degree, and the highest degree of any term is one.

What is the general form of a linear equation in two variables?

The general form of a linear equation in two variables is ax + by = c, where a, b, and c are real numbers and a and b are not zero.

How do you find the slope and y-intercept from the standard form of a linear equation?

To find the slope (m) and y-intercept (b) from the standard form of a linear equation ax + by = c, you first isolate y by subtracting 'ax' from both sides and then divide by 'b' to get y = (-c/a)x + c/b.

Can you provide an example of how to construct a table of values for a linear equation?

To construct a table of values for a linear equation like 2x + 4y = 20, you can assign values to x and solve for y to find corresponding ordered pairs (x, y) that satisfy the equation.

How do you determine the solutions of linear equations in two variables?

The solutions of linear equations in two variables are the ordered pairs (x, y) that make the equation true when substituted into the equation.

What is the significance of the infinitely many solutions for a linear equation in two variables?

The infinitely many solutions for a linear equation in two variables indicate that there are multiple points that satisfy the equation, and when graphed, they all lie on a straight line.