Grade 8 Math Q1 Ep10: Linear Equation

Summary

Teacher Joshua from Depped TV introduces linear equations in two variables, using a relatable scenario of Anna and Ben bringing chairs for a charity event. The video explains how to solve for variables in equations like x + y = 10, transforming them into standard form. It demonstrates finding solutions through substitution and plotting these on a rectangular coordinate system, highlighting the concept of intercepts. The lesson also touches on linear equations in one variable, their solutions, and how they graph as vertical or horizontal lines, encouraging practice and a positive learning attitude.

Takeaways

• 📘 The video is a mathematics learning guide for grade 8 students, focusing on linear equations.
• 👨‍🏫 Teacher Joshua introduces the concept of linear equations and their solutions through a real-world scenario involving Anna and Ben bringing chairs.
• 🔢 The script explains how to set up and solve equations to find the number of chairs each person brought, using variables x and y.
• 📉 The video demonstrates solving equations using properties of equality, such as addition, subtraction, and multiplication.
• 📚 It defines a linear equation in two variables and explains the significance of coefficients and constants.
• 📝 The script shows how to write a linear equation in standard form and provides examples for practice.
• 📈 The video teaches how to find solutions to linear equations by substituting values and using the properties of equality.
• 📊 It explains the concept of ordered pairs and how they relate to points on a graph, introducing the rectangular coordinate system.
• 📐 The script describes how to plot points on a graph and connect them to form a line representing the solutions to a linear equation.
• 📖 It discusses the concept of intercepts and how they are found when a graph intersects the x and y axes.
• 🔍 The video concludes with a reminder to practice and provides resources for further learning on the topic.

Q & A

What is the main topic discussed in the video script?

The main topic discussed in the video script is the concept of linear equations in two variables, including how to solve them and graph their solutions.

What is the equation that represents the total number of chairs brought by Anna and Ben?

The equation representing the total number of chairs brought by Anna and Ben is x + y = 10, where x is the number of chairs Ben brought and y is the number of chairs Anna brought.

How many chairs did Ben bring if Anna brought in three chairs?

If Anna brought in three chairs, Ben brought in seven chairs, as solving the equation x + 3 = 10 gives x = 7.

What is the equation in standard form when Ben brought in four chairs?

When Ben brought in four chairs, the equation in standard form is 4 + y = 10, and solving for y gives y = 6, meaning Anna brought in six chairs.

How many chairs did Anna bring in if Ben brought nine chairs?

If Ben brought nine chairs, Anna brought one chair, as solving the equation 9 + y = 10 gives y = 1.

What is a linear equation in two variables?

A linear equation in two variables is an equation that contains two variables, each raised to the power of one, and the equation is of the first degree. It can be written in the form ax + by = c, where a, b, and c are real numbers and a and b are not both zero.

How do you write the equation 4y = 6 - 5x in standard form?

To write the equation 4y = 6 - 5x in standard form, you rearrange it to 5x + 4y = 6 by applying the additive inverse property and the addition property of equality.

What is the solution to the equation x - 2y = 6 when x is 4?

When x is 4, the solution to the equation x - 2y = 6 is y = -1, as substituting x = 4 into the equation gives 4 - 2y = 6, which simplifies to y = -1.

What are the ordered pairs that are solutions to the equation x - 2y = 6?

The ordered pairs that are solutions to the equation x - 2y = 6 are (4, -1), (2, -2), and (8, 1).

How do you plot the solutions of a linear equation on a rectangular coordinate system?

To plot the solutions of a linear equation on a rectangular coordinate system, you identify the x and y values from the solutions (ordered pairs), then mark these points on the coordinate plane. If you connect these points, they form a straight line representing the equation's solutions.

What are the intercepts of a linear equation graph?

The intercepts of a linear equation graph are the points where the line intersects the x-axis (x-intercept) and the y-axis (y-intercept). These points have coordinates where one of the variables (x or y) is zero.

What does the graph of the equation x = 5 look like?

The graph of the equation x = 5 is a vertical line, as for any value of y, the value of x remains 5.

What does the graph of the equation y = 5 look like?

The graph of the equation y = 5 is a horizontal line, as for any value of x, the value of y remains 5.