Converting the equation Y = 4x - 7 to standard form is a straightforward process that can be completed in three steps. The standard form of a linear equation is Ax + By = C, where A, B, and C are constants. Here's how to convert the given equation:
Y = 4x - 7
Step 1: Move the constant term to the right-hand side of the equation.
To do this, we'll add 7 to both sides of the equation, which results in:
Y + 7 = 4x
Step 2: Rearrange the equation so that the variables (x and y) are on one side.
By subtracting 4x from both sides of the equation, we get:
-4x + Y + 7 = 0
Step 3: Rearrange the equation so that the x-term comes first, followed by the y-term, and then the constant term.
We'll rearrange the equation to get:
-4x + Y = -7
And finally, to conform to the standard form, we'll add a coefficient of 1 to the y-term:
-4x + 1y = -7
Or, more simply:
-4x + y = -7
This is the equation in standard form.
Benefits of Standard Form
Converting equations to standard form provides several benefits, including:
- Simplifying the process of solving systems of linear equations
- Making it easier to identify the x-intercept and y-intercept of the line
- Providing a consistent format for comparing and contrasting different linear equations
Working Mechanism of Standard Form
The standard form of a linear equation works by providing a consistent format for expressing the relationship between the variables x and y. By rearranging the equation to conform to the standard form, we can easily identify the coefficients of x and y, as well as the constant term.
Steps to Convert to Standard Form
To convert an equation to standard form, follow these steps:
- Move the constant term to the right-hand side of the equation.
- Rearrange the equation so that the variables (x and y) are on one side.
- Rearrange the equation so that the x-term comes first, followed by the y-term, and then the constant term.
Examples of Standard Form
Here are a few examples of linear equations in standard form:
- 2x + 3y = 12
- x - 2y = -3
- 4x - y = 9
Frequently Asked Questions
What is the standard form of a linear equation?
+The standard form of a linear equation is Ax + By = C, where A, B, and C are constants.
Why is it important to convert equations to standard form?
+Converting equations to standard form provides several benefits, including simplifying the process of solving systems of linear equations, making it easier to identify the x-intercept and y-intercept of the line, and providing a consistent format for comparing and contrasting different linear equations.
How do I convert an equation to standard form?
+To convert an equation to standard form, follow these steps: move the constant term to the right-hand side of the equation, rearrange the equation so that the variables (x and y) are on one side, and rearrange the equation so that the x-term comes first, followed by the y-term, and then the constant term.
By following these steps and understanding the benefits of standard form, you'll be able to convert equations with ease and solve systems of linear equations with confidence.
Note: If you have any questions or need further clarification, feel free to ask in the comments section below!