A Line Has A Slope Of -7 And A $y$-intercept Of $\frac{1}{2}$. Write Its Equation In Slope-intercept Form.Write Your Answer Using Integers, Proper Fractions, And Improper Fractions In Simplest Form.

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Introduction

In mathematics, the slope-intercept form of a line is a fundamental concept that helps us understand the relationship between the slope and the y-intercept of a line. The slope-intercept form of a line is given by the equation y = mx + b, where m is the slope and b is the y-intercept. In this article, we will discuss how to write the equation of a line with a given slope and y-intercept in slope-intercept form.

Understanding the Slope-Intercept Form

The slope-intercept form of a line is given by the equation y = mx + b, where m is the slope and b is the y-intercept. The slope of a line is a measure of how steep it is, and it is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line. The y-intercept of a line is the point where the line intersects the y-axis.

Writing the Equation of a Line with a Given Slope and Y-Intercept

To write the equation of a line with a given slope and y-intercept, we can use the slope-intercept form of a line. The slope-intercept form of a line is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Example 1: A Line with a Slope of -7 and a Y-Intercept of 1/2

Let's consider a line with a slope of -7 and a y-intercept of 1/2. We can write the equation of this line in slope-intercept form as follows:

y = -7x + 1/2

In this equation, -7 is the slope and 1/2 is the y-intercept.

Simplifying the Equation

We can simplify the equation by multiplying both sides by 2 to eliminate the fraction:

2y = -14x + 1

Now, we can rewrite the equation in slope-intercept form as follows:

y = -7x + 1/2

Example 2: A Line with a Slope of 3 and a Y-Intercept of -2

Let's consider a line with a slope of 3 and a y-intercept of -2. We can write the equation of this line in slope-intercept form as follows:

y = 3x - 2

In this equation, 3 is the slope and -2 is the y-intercept.

Simplifying the Equation

We can simplify the equation by adding 2 to both sides:

y + 2 = 3x

Now, we can rewrite the equation in slope-intercept form as follows:

y = 3x - 2

Conclusion

In conclusion, writing the equation of a line with a given slope and y-intercept in slope-intercept form is a straightforward process. We can use the slope-intercept form of a line, which is given by the equation y = mx + b, where m is the slope and b is the y-intercept. By substituting the given slope and y-intercept into this equation, we can write the equation of the line in slope-intercept form.

Frequently Asked Questions

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

A: The slope-intercept form of a line is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Q: How do I write the equation of a line with a given slope and y-intercept in slope-intercept form?

A: To write the equation of a line with a given slope and y-intercept in slope-intercept form, you can use the slope-intercept form of a line, which is given by the equation y = mx + b. Substitute the given slope and y-intercept into this equation to write the equation of the line in slope-intercept form.

Q: Can I simplify the equation of a line in slope-intercept form?

A: Yes, you can simplify the equation of a line in slope-intercept form by multiplying both sides of the equation by a common factor or by adding or subtracting a constant from both sides of the equation.

References

Keywords

  • Slope-intercept form
  • Slope
  • Y-intercept
  • Equation of a line
  • Mathematics

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Introduction

In our previous article, we discussed how to write the equation of a line with a given slope and y-intercept in slope-intercept form. In this article, we will answer some frequently asked questions related to this topic.

Q&A

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

A: The slope-intercept form of a line is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Q: How do I write the equation of a line with a given slope and y-intercept in slope-intercept form?

A: To write the equation of a line with a given slope and y-intercept in slope-intercept form, you can use the slope-intercept form of a line, which is given by the equation y = mx + b. Substitute the given slope and y-intercept into this equation to write the equation of the line in slope-intercept form.

Q: Can I simplify the equation of a line in slope-intercept form?

A: Yes, you can simplify the equation of a line in slope-intercept form by multiplying both sides of the equation by a common factor or by adding or subtracting a constant from both sides of the equation.

Q: What is the difference between the slope-intercept form and the standard form of a line?

A: The slope-intercept form of a line is given by the equation y = mx + b, where m is the slope and b is the y-intercept. The standard form of a line is given by the equation Ax + By = C, where A, B, and C are constants. The slope-intercept form is more useful for finding the equation of a line when the slope and y-intercept are known, while the standard form is more useful for finding the equation of a line when the x and y intercepts are known.

Q: Can I use the slope-intercept form to find the equation of a line when the x and y intercepts are known?

A: No, you cannot use the slope-intercept form to find the equation of a line when the x and y intercepts are known. The slope-intercept form is more useful for finding the equation of a line when the slope and y-intercept are known.

Q: How do I find the slope and y-intercept of a line when the equation is given in standard form?

A: To find the slope and y-intercept of a line when the equation is given in standard form, you can rewrite the equation in slope-intercept form by dividing both sides of the equation by the coefficient of x and then subtracting the constant term from both sides of the equation.

Q: Can I use the slope-intercept form to find the equation of a line when the slope is zero?

A: Yes, you can use the slope-intercept form to find the equation of a line when the slope is zero. In this case, the equation of the line will be of the form y = b, where b is the y-intercept.

Q: Can I use the slope-intercept form to find the equation of a line when the slope is undefined?

A: No, you cannot use the slope-intercept form to find the equation of a line when the slope is undefined. The slope-intercept form is only useful for finding the equation of a line when the slope is a real number.

Conclusion

In conclusion, the slope-intercept form of a line is a useful tool for finding the equation of a line when the slope and y-intercept are known. By using the slope-intercept form, you can write the equation of a line in a simple and straightforward way.

Frequently Asked Questions

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

A: The slope-intercept form of a line is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Q: How do I write the equation of a line with a given slope and y-intercept in slope-intercept form?

A: To write the equation of a line with a given slope and y-intercept in slope-intercept form, you can use the slope-intercept form of a line, which is given by the equation y = mx + b. Substitute the given slope and y-intercept into this equation to write the equation of the line in slope-intercept form.

Q: Can I simplify the equation of a line in slope-intercept form?

A: Yes, you can simplify the equation of a line in slope-intercept form by multiplying both sides of the equation by a common factor or by adding or subtracting a constant from both sides of the equation.

References

Keywords

  • Slope-intercept form
  • Slope
  • Y-intercept
  • Equation of a line
  • Mathematics