Convert The Following Lines From Standard Form To Slope-intercept Form:1. \[$-2x + Y = -4\$\]2. \[$y = 2x + 3\$\]3. \[$y = 2x - 4\$\]4. \[$3y = -x + 3\$\]Please Provide The Solutions For Each Equation In The Format

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Introduction

In mathematics, equations can be represented in various forms, including standard form and slope-intercept form. The standard form of a linear equation is typically written as Ax + By = C, where A, B, and C are constants. On the other hand, the slope-intercept form is written as y = mx + b, where m is the slope and b is the y-intercept. In this article, we will discuss how to convert equations from standard form to slope-intercept form.

Converting the First Equation

The first equation is given as -2x + y = -4. To convert this equation to slope-intercept form, we need to isolate y on one side of the equation.

Step 1: Add 2x to both sides of the equation

By adding 2x to both sides of the equation, we get:

y = -2x + 4

Step 2: Rewrite the equation in slope-intercept form

The equation is now in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is -2 and the y-intercept is 4.

Solution 1

The first equation -2x + y = -4 can be rewritten in slope-intercept form as:

y = -2x + 4

Converting the Second Equation

The second equation is given as y = 2x + 3. This equation is already in slope-intercept form, so we don't need to convert it.

Solution 2

The second equation y = 2x + 3 is already in slope-intercept form.

Converting the Third Equation

The third equation is given as y = 2x - 4. This equation is also already in slope-intercept form, so we don't need to convert it.

Solution 3

The third equation y = 2x - 4 is already in slope-intercept form.

Converting the Fourth Equation

The fourth equation is given as 3y = -x + 3. To convert this equation to slope-intercept form, we need to isolate y on one side of the equation.

Step 1: Divide both sides of the equation by 3

By dividing both sides of the equation by 3, we get:

y = (-1/3)x + 1

Step 2: Rewrite the equation in slope-intercept form

The equation is now in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is -1/3 and the y-intercept is 1.

Solution 4

The fourth equation 3y = -x + 3 can be rewritten in slope-intercept form as:

y = (-1/3)x + 1

Conclusion

Introduction

In our previous article, we discussed how to convert equations from standard form to slope-intercept form. In this article, we will provide a Q&A section to help clarify any doubts and provide additional information on this topic.

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.

Q: What is the slope-intercept form of a linear equation?

A: The slope-intercept form of a linear equation is written as y = mx + b, where m is the slope and b is the y-intercept.

Q: How do I convert an equation from standard form to slope-intercept form?

A: To convert an equation from standard form to slope-intercept form, you need to isolate y on one side of the equation. This can be done by adding or subtracting the same value to both sides of the equation, or by multiplying or dividing both sides of the equation by the same non-zero value.

Q: What is the slope of an equation in slope-intercept form?

A: The slope of an equation in slope-intercept form is the value of m, which is the coefficient of x.

Q: What is the y-intercept of an equation in slope-intercept form?

A: The y-intercept of an equation in slope-intercept form is the value of b, which is the constant term.

Q: Can I convert an equation from slope-intercept form to standard form?

A: Yes, you can convert an equation from slope-intercept form to standard form by rearranging the terms. For example, if you have the equation y = 2x + 3, you can rewrite it as 2x + y = 3.

Q: What are some common mistakes to avoid when converting equations from standard form to slope-intercept form?

A: Some common mistakes to avoid when converting equations from standard form to slope-intercept form include:

  • Not isolating y on one side of the equation
  • Not multiplying or dividing both sides of the equation by the same non-zero value
  • Not checking for any errors in the conversion process

Q: Can I use a calculator to convert equations from standard form to slope-intercept form?

A: Yes, you can use a calculator to convert equations from standard form to slope-intercept form. However, it's always a good idea to double-check your work to ensure that the conversion is correct.

Conclusion

In this article, we provided a Q&A section to help clarify any doubts and provide additional information on converting equations from standard form to slope-intercept form. We hope that this article has been helpful in understanding this important concept in mathematics.

Additional Resources

  • Mathway: A online math problem solver that can help you convert equations from standard form to slope-intercept form.
  • Khan Academy: A free online learning platform that provides video lessons and practice exercises on converting equations from standard form to slope-intercept form.
  • Wolfram Alpha: A online calculator that can help you convert equations from standard form to slope-intercept form.