Understanding And Solving "X 3Y 6" In Slope-Intercept Form

Write the equation ?x 3y = 6 in slope intercept form? mfacourses826 from mfacourses826.web.fc2.com

Introduction

As a professional teacher, it's important to teach students about different types of equations in algebra. One of the most common equations is the slope-intercept form, which is used to graph linear equations. In this article, we will be focusing on the equation "x 3y 6" and how to convert it into slope-intercept form.

Slope-Intercept Form

Before we dive into solving "x 3y 6" in slope-intercept form, let's first understand what it means. Slope-intercept form is a way to write a linear equation in the form y = mx + b, where m is the slope and b is the y-intercept. The slope is the rate of change of the line, while the y-intercept is where the line crosses the y-axis.

Solving "x 3y 6" in Slope-Intercept Form

To convert "x 3y 6" into slope-intercept form, we need to isolate the y variable on one side of the equation. Let's start by subtracting x from both sides:

x - x + 3y = 6

Now, let's divide both sides by 3 to isolate y:

3y/3 = 6/3

y = 2

So, the equation "x 3y 6" in slope-intercept form is y = 2. This means the line is a horizontal line that crosses the y-axis at y = 2.

Understanding the Graph

Now that we have the equation in slope-intercept form, we can easily graph it. Since the slope is 0, the line is horizontal. The y-intercept is 2, so the line crosses the y-axis at (0, 2).

Graphing the Line

To graph the line, we can plot the y-intercept at (0, 2) and draw a horizontal line through it. The line will look like this:

Real-World Application

Linear equations in slope-intercept form are used in many real-world situations, such as calculating the cost of a phone plan or the speed of a car. In the case of "x 3y 6", we can use it to represent a situation where y is a constant value. For example, if y represents the number of hours a store is open and y = 2, this means the store is open for 2 hours every day.

Conclusion

Understanding and solving equations in slope-intercept form is an important skill in algebra. By converting "x 3y 6" into slope-intercept form, we were able to graph the line and understand its real-world application. As a teacher, it's important to teach students how to solve different types of equations and how they can be used in real-life situations.