Identify And Clearly Label The Slope And Y-intercept For The Equation In Slope-intercept Form:$y = \frac{3}{4}x - 5$Choose The Correct Answer From The Options Below:A. Slope Is $\frac{3}{4}$ And The Y-intercept Is $(0,

Introduction

In mathematics, the slope-intercept form of a linear equation is a powerful tool for representing lines on a coordinate plane. This form, denoted as $y = mx + b$, consists of two essential components: the slope ($m$) and the y-intercept ($b$). In this article, we will delve into the world of slope-intercept form and explore how to identify and clearly label the slope and y-intercept for a given equation.

What is Slope-Intercept Form?

The slope-intercept form of a linear equation is a way to express a line in terms of its slope and y-intercept. The general form of a slope-intercept equation is:

$$y = mx + b$$

where:

• $m$ represents the slope of the line
• $b$ represents the y-intercept of the line

Identifying Slope and Y-Intercept

To identify the slope and y-intercept of a line in slope-intercept form, we need to look at the equation and extract the values of $m$ and $b$. Let's consider the equation:

$$y = \frac{3}{4}x - 5$$

In this equation, the slope ($m$) is $\frac{3}{4}$, and the y-intercept ($b$) is $-5$. To identify these values, we can follow these steps:

1. Identify the slope: The slope is the coefficient of the $x$ term. In this case, the coefficient of $x$ is $\frac{3}{4}$, so the slope is $\frac{3}{4}$.
2. Identify the y-intercept: The y-intercept is the constant term. In this case, the constant term is $-5$, so the y-intercept is $-5$.

Choosing the Correct Answer

Now that we have identified the slope and y-intercept, we can choose the correct answer from the options below:

A. Slope is $\frac{3}{4}$ and the y-intercept is $(0, -5)$

B. Slope is $\frac{3}{4}$ and the y-intercept is $-5$

C. Slope is $-5$ and the y-intercept is $\frac{3}{4}$

D. Slope is $-5$ and the y-intercept is $(0, \frac{3}{4})$

The correct answer is:

A. Slope is $\frac{3}{4}$ and the y-intercept is $(0, -5)$

Conclusion

In conclusion, identifying the slope and y-intercept of a line in slope-intercept form is a crucial skill in mathematics. By following the steps outlined in this article, we can easily identify the slope and y-intercept of a line and choose the correct answer from a set of options. Whether you're a student or a teacher, understanding slope-intercept form is essential for success in mathematics.

Frequently Asked Questions

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

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

Q: How do I identify the slope and y-intercept of a line in slope-intercept form?

A: To identify the slope and y-intercept, look at the equation and extract the values of $m$ and $b$. The slope is the coefficient of the $x$ term, and the y-intercept is the constant term.

Q: What is the y-intercept of the line $y = \frac{3}{4}x - 5$?

A: The y-intercept of the line $y = \frac{3}{4}x - 5$ is $-5$.

Q: What is the slope of the line $y = \frac{3}{4}x - 5$?

A: The slope of the line $y = \frac{3}{4}x - 5$ is $\frac{3}{4}$.

Q: How do I choose the correct answer from a set of options?

Introduction

In our previous article, we explored the concept of slope-intercept form and learned how to identify the slope and y-intercept of a line. In this article, we will delve deeper into the world of slope-intercept form and provide a comprehensive guide to identifying slope and y-intercept.

Frequently Asked Questions

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

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

Q: How do I identify the slope and y-intercept of a line in slope-intercept form?

A: To identify the slope and y-intercept, look at the equation and extract the values of $m$ and $b$. The slope is the coefficient of the $x$ term, and the y-intercept is the constant term.

Q: What is the y-intercept of the line $y = \frac{3}{4}x - 5$?

A: The y-intercept of the line $y = \frac{3}{4}x - 5$ is $-5$.

Q: What is the slope of the line $y = \frac{3}{4}x - 5$?

A: The slope of the line $y = \frac{3}{4}x - 5$ is $\frac{3}{4}$.

Q: How do I choose the correct answer from a set of options?

A: To choose the correct answer, identify the slope and y-intercept of the line and match them with the options provided.

Q: What is the difference between the slope and y-intercept?

A: The slope represents the rate of change of the line, while the y-intercept represents the point where the line intersects the y-axis.

Q: How do I graph a line in slope-intercept form?

A: To graph a line in slope-intercept form, use the slope and y-intercept to find two points on the line. Then, draw a line through the two points to represent the line.

Q: Can a line have a slope of zero?

A: Yes, a line can have a slope of zero. This occurs when the line is horizontal and intersects the y-axis at a single point.

Q: Can a line have a y-intercept of zero?

A: Yes, a line can have a y-intercept of zero. This occurs when the line intersects the x-axis at a single point.

Q: How do I find the equation of a line in slope-intercept form?

A: To find the equation of a line in slope-intercept form, use the slope and a point on the line to find the y-intercept. Then, use the slope and y-intercept to write the equation in slope-intercept form.

Additional Resources

• Slope-Intercept Form Calculator: A calculator that can help you find the slope and y-intercept of a line in slope-intercept form.
• Graphing Calculator: A calculator that can help you graph a line in slope-intercept form.
• Mathematics Textbook: A textbook that provides a comprehensive guide to mathematics, including slope-intercept form.

Conclusion

In conclusion, identifying the slope and y-intercept of a line in slope-intercept form is a crucial skill in mathematics. By following the steps outlined in this article, you can easily identify the slope and y-intercept of a line and choose the correct answer from a set of options. Whether you're a student or a teacher, understanding slope-intercept form is essential for success in mathematics.

Final Tips

• Practice, Practice, Practice: The more you practice identifying the slope and y-intercept of a line in slope-intercept form, the more comfortable you will become with the concept.
• Use Online Resources: There are many online resources available that can help you learn about slope-intercept form, including calculators and graphing tools.
• Seek Help When Needed: Don't be afraid to ask for help if you're struggling with a concept. Whether it's a teacher, a tutor, or a classmate, there are many resources available to help you succeed.