Convert The Following Equation Into Standard Form.$y = 16x + 12$\[?]x + Y =$
Introduction
In mathematics, linear equations are a fundamental concept that plays a crucial role in various fields, including algebra, geometry, and calculus. A linear equation is an equation in which the highest power of the variable(s) is 1. In this article, we will focus on converting a given linear equation into standard form. The standard form of a linear equation is typically written as ax + by = c, where a, b, and c are constants, and x and y are variables.
Understanding the Given Equation
The given equation is y = 16x + 12. This equation is in slope-intercept form, where the slope of the line is 16 and the y-intercept is 12. To convert this equation into standard form, we need to isolate the variable x and move all the terms involving x to one side of the equation.
Converting the Equation to Standard Form
To convert the equation y = 16x + 12 into standard form, we need to follow these steps:
- Isolate the variable y: The given equation already has y isolated on the left-hand side.
- Move the constant term to the right-hand side: We can do this by subtracting 12 from both sides of the equation.
Step 1: Isolate the Variable y
The given equation is y = 16x + 12. Since y is already isolated on the left-hand side, we can proceed to the next step.
Step 2: Move the Constant Term to the Right-Hand Side
To move the constant term to the right-hand side, we subtract 12 from both sides of the equation:
y - 12 = 16x
Step 3: Rearrange the Equation to Standard Form
Now that we have the constant term on the right-hand side, we can rearrange the equation to standard form by swapping the left-hand and right-hand sides:
16x = y - 12
However, we want to express the equation in the form ax + by = c. To do this, we need to multiply both sides of the equation by -1 to get:
-16x = -y + 12
Now, we can rewrite the equation as:
16x + y = 12
Conclusion
In this article, we converted the given linear equation y = 16x + 12 into standard form. We followed the steps of isolating the variable y, moving the constant term to the right-hand side, and rearranging the equation to standard form. The resulting equation in standard form is 16x + y = 12.
Key Takeaways
- Linear equations can be converted from slope-intercept form to standard form by isolating the variable and moving the constant term to the right-hand side.
- The standard form of a linear equation is typically written as ax + by = c, where a, b, and c are constants, and x and y are variables.
- Converting a linear equation to standard form can help in solving systems of linear equations and graphing linear functions.
Frequently Asked Questions
Q: What is the standard form of a linear equation?
A: The standard form of a linear equation is typically written as ax + by = c, where a, b, and c are constants, and x and y are variables.
Q: How do I convert a linear equation from slope-intercept form to standard form?
A: To convert a linear equation from slope-intercept form to standard form, you need to isolate the variable and move the constant term to the right-hand side.
Q: What is the difference between slope-intercept form and standard form?
Introduction
In our previous article, we discussed how to convert a linear equation from slope-intercept form to standard form. In this article, we will provide a comprehensive Q&A section to help you better understand the concept and address any questions you may have.
Q: What is the standard form of a linear equation?
A: The standard form of a linear equation is typically written as ax + by = c, where a, b, and c are constants, and x and y are variables.
Q: How do I convert a linear equation from slope-intercept form to standard form?
A: To convert a linear equation from slope-intercept form to standard form, you need to follow these steps:
- Isolate the variable y: The given equation should have y isolated on the left-hand side.
- Move the constant term to the right-hand side: Subtract the constant term from both sides of the equation.
- Rearrange the equation to standard form: Swap the left-hand and right-hand sides of the equation.
Q: What is the difference between slope-intercept form and standard form?
A: Slope-intercept form is written as y = mx + b, where m is the slope and b is the y-intercept. Standard form is written as ax + by = c, where a, b, and c are constants, and x and y are variables.
Q: Can I convert a linear equation from standard form to slope-intercept form?
A: Yes, you can convert a linear equation from standard form to slope-intercept form by following these steps:
- Isolate the variable x: The given equation should have x isolated on the left-hand side.
- Move the constant term to the right-hand side: Subtract the constant term from both sides of the equation.
- Rearrange the equation to slope-intercept form: Swap the left-hand and right-hand sides of the equation.
Q: How do I graph a linear equation in standard form?
A: To graph a linear equation in standard form, you can follow these steps:
- Identify the coefficients: Identify the coefficients a, b, and c in the equation.
- Determine the slope: The slope of the line is given by -a/b.
- Determine the y-intercept: The y-intercept of the line is given by c/b.
- Plot the line: Plot the line using the slope and y-intercept.
Q: Can I use a calculator to convert a linear equation from slope-intercept form to standard form?
A: Yes, you can use a calculator to convert a linear equation from slope-intercept form to standard form. Most graphing calculators have a built-in function to convert equations from slope-intercept form to standard form.
Q: What are some common mistakes to avoid when converting linear equations?
A: Some common mistakes to avoid when converting linear equations include:
- Not isolating the variable: Make sure to isolate the variable on the left-hand side of the equation.
- Not moving the constant term: Make sure to move the constant term to the right-hand side of the equation.
- Not rearranging the equation: Make sure to rearrange the equation to standard form.
Conclusion
In this article, we provided a comprehensive Q&A section to help you better understand the concept of converting linear equations from slope-intercept form to standard form. We also discussed how to graph a linear equation in standard form and common mistakes to avoid when converting linear equations.