Convert Y = 3x - 10 To Standard Form

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The process of converting an equation from slope-intercept form (y = mx + b) to standard form (Ax + By = C) is a straightforward one. In this case, we want to convert the equation Y = 3x - 10 to standard form. Here's how to do it:

Understanding the Equation

The given equation is in slope-intercept form, where m represents the slope and b represents the y-intercept. In this case, the equation Y = 3x - 10 tells us that the slope (m) is 3 and the y-intercept (b) is -10.

Converting to Standard Form

To convert the equation to standard form, we need to move the x term to the left-hand side of the equation and the constant term to the right-hand side. We can do this by adding 10 to both sides of the equation:

Y = 3x - 10 Y + 10 = 3x

Next, we want to get the x term by itself on the left-hand side. To do this, we can subtract 3x from both sides of the equation:

-3x + Y + 10 = 0

Now, we can rearrange the terms to get the equation in standard form:

-3x + Y = -10

Standard Form Equation

The equation Y = 3x - 10 in standard form is -3x + Y = -10. This equation has the same solution set as the original equation, but it is written in a different form.

Benefits of Standard Form

There are several benefits to writing an equation in standard form. For example, it can make it easier to:

• Find the x-intercept and y-intercept of a line
• Graph a line using the intercepts
• Solve systems of linear equations
• Find the equation of a line perpendicular to a given line

Conclusion

In conclusion, converting an equation from slope-intercept form to standard form is a simple process that involves moving the x term to the left-hand side and the constant term to the right-hand side. The resulting equation has the same solution set as the original equation, but it is written in a different form. Understanding how to convert between different forms of a linear equation is an important skill in algebra and is used in a variety of applications.

Takeaways

• The equation Y = 3x - 10 in standard form is -3x + Y = -10.
• Converting to standard form involves moving the x term to the left-hand side and the constant term to the right-hand side.
• Standard form is useful for finding the x-intercept and y-intercept of a line, graphing a line using the intercepts, solving systems of linear equations, and finding the equation of a line perpendicular to a given line.

We hope this article has helped you understand how to convert an equation from slope-intercept form to standard form. Do you have any questions or would you like to share your thoughts on this topic? Please leave a comment below.