Converting 5x 3y 12 To Slope Intercept Form

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Understanding the fundamentals of linear equations and their various forms is crucial in mathematics and its applications. One of the most commonly used forms of a linear equation is the slope-intercept form, which is y = mx + b, where m represents the slope of the line, and b represents the y-intercept. The slope-intercept form is useful for graphing lines and understanding their behavior.

When we are given an equation in the form of ax + by = c, we can convert it into the slope-intercept form. To do this, we need to isolate y on one side of the equation. The given equation 5x + 3y = 12 will be converted into slope-intercept form.

Converting the Equation

The equation 5x + 3y = 12 can be converted into the slope-intercept form by isolating y. To do this, we subtract 5x from both sides of the equation, resulting in 3y = -5x + 12. Then, we divide both sides by 3, which gives us y = (-5/3)x + 4.

This equation is now in the slope-intercept form, y = mx + b. The slope of the line is -5/3, and the y-intercept is 4.

Understanding the Slope and Y-Intercept

The slope of a line, denoted by m, represents the rate of change of y with respect to x. In this case, the slope is -5/3, which means that for every 3-unit increase in x, y decreases by 5 units. The slope can be positive, negative, or zero, and it affects the orientation of the line.

The y-intercept, denoted by b, is the point at which the line intersects the y-axis. In this case, the y-intercept is 4, which means that the line crosses the y-axis at the point (0, 4).

Benefits of Slope-Intercept Form

The slope-intercept form has several benefits, including:

• Easy graphing: The slope-intercept form makes it easy to graph lines by plotting the y-intercept and using the slope to determine the direction of the line.
• Understanding behavior: The slope-intercept form helps us understand the behavior of the line, including its orientation and intercepts.
• Simplifying equations: The slope-intercept form can simplify complex equations by isolating y and making it easier to solve for x.

Real-World Applications

The slope-intercept form has numerous real-world applications, including:

• Physics: The slope-intercept form is used to model the motion of objects, including their velocity and acceleration.
• Economics: The slope-intercept form is used to model the behavior of markets, including supply and demand curves.
• Computer Science: The slope-intercept form is used in computer graphics and game development to create realistic simulations.

Conclusion

In conclusion, converting the equation 5x + 3y = 12 to slope-intercept form is a useful skill that can help us understand the behavior of lines and their applications in real-world scenarios. By isolating y and identifying the slope and y-intercept, we can gain valuable insights into the equation and its graph.

If you have any questions or need further clarification, please don't hesitate to ask. Share your thoughts and experiences with converting equations to slope-intercept form in the comments below.