Which Ordered Pair Represents The $y$-intercept Of The Graph Of The Equation $y=-4x-7$?A. $ ( 0 , − 7 ) (0, -7) ( 0 , − 7 ) [/tex] B. $(-7, 0)$ C. $(-4, 0)$ D. $ ( 0 , − 4 ) (0, -4) ( 0 , − 4 ) [/tex]

Mar 10, 2025 by ADMIN 212 views

**Understanding the y-Intercept of a Linear Equation**

Introduction

In mathematics, the y-intercept of a linear equation is a crucial concept that helps us understand the behavior of the graph of the equation. The y-intercept is the point at which the graph intersects the y-axis, and it is denoted by the ordered pair (0, y). In this article, we will explore the concept of the y-intercept and determine which ordered pair represents the y-intercept of the graph of the equation y = -4x - 7.

What is the y-Intercept?

The y-intercept is the point on the graph where the x-coordinate is zero. In other words, it is the point at which the graph intersects the y-axis. The y-intercept is denoted by the ordered pair (0, y), where y is the value of the function at x = 0.

Finding the y-Intercept of a Linear Equation

To find the y-intercept of a linear equation, we can substitute x = 0 into the equation and solve for y. This is because the y-intercept occurs when the x-coordinate is zero, and substituting x = 0 into the equation will give us the value of y at that point.

Example: Finding the y-Intercept of the Equation y = -4x - 7

Let's find the y-intercept of the equation y = -4x - 7. To do this, we will substitute x = 0 into the equation and solve for y.

y = -4x - 7 y = -4(0) - 7 y = -7

Therefore, the y-intercept of the graph of the equation y = -4x - 7 is the point (0, -7).

Which Ordered Pair Represents the y-Intercept?

Now that we have found the y-intercept of the equation y = -4x - 7, we can determine which ordered pair represents the y-intercept. The correct answer is the ordered pair that matches the y-intercept we found.

A. (0, -7) B. (-7, 0) C. (-4, 0) D. (0, -4)

The correct answer is A. (0, -7), because this is the ordered pair that represents the y-intercept of the graph of the equation y = -4x - 7.

Conclusion

In conclusion, the y-intercept of a linear equation is the point at which the graph intersects the y-axis. To find the y-intercept, we can substitute x = 0 into the equation and solve for y. In this article, we found the y-intercept of the equation y = -4x - 7 and determined which ordered pair represents the y-intercept. The correct answer is A. (0, -7).

Frequently Asked Questions

What is the y-intercept of a linear equation?
How do I find the y-intercept of a linear equation?
Which ordered pair represents the y-intercept of the graph of the equation y = -4x - 7?

Answers to Frequently Asked Questions

The y-intercept of a linear equation is the point at which the graph intersects the y-axis.
To find the y-intercept of a linear equation, substitute x = 0 into the equation and solve for y.
The correct answer is A. (0, -7).

Additional Resources

Khan Academy: Y-Intercept
Mathway: Y-Intercept
Wolfram Alpha: Y-Intercept

References

Algebra: Structure and Method Book 1 by Marvin L. Bittinger
Algebra and Trigonometry by James Stewart
Calculus: Early Transcendentals by James Stewart
Y-Intercept Q&A: Frequently Asked Questions and Answers =====================================================

Introduction

In our previous article, we explored the concept of the y-intercept of a linear equation and determined which ordered pair represents the y-intercept of the graph of the equation y = -4x - 7. In this article, we will answer some of the most frequently asked questions about the y-intercept.

Q&A: Y-Intercept

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

A: The y-intercept of a linear equation is the point at which the graph intersects the y-axis. It is denoted by the ordered pair (0, y), where y is the value of the function at x = 0.

Q: How do I find the y-intercept of a linear equation?

A: To find the y-intercept of a linear equation, substitute x = 0 into the equation and solve for y. This will give you the value of y at x = 0, which is the y-intercept.

Q: What is the significance of the y-intercept?

A: The y-intercept is significant because it gives us information about the behavior of the graph of the equation. It tells us where the graph intersects the y-axis, which can be useful in understanding the equation's behavior.

Q: Can the y-intercept be negative?

A: Yes, the y-intercept can be negative. In fact, the y-intercept can be any real number, positive or negative.

Q: Can the y-intercept be zero?

A: Yes, the y-intercept can be zero. This occurs when the equation is of the form y = 0, which means that the graph intersects the y-axis at the origin (0, 0).

Q: How do I determine which ordered pair represents the y-intercept?

A: To determine which ordered pair represents the y-intercept, substitute x = 0 into the equation and solve for y. The ordered pair that matches the y-intercept is the correct answer.

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

A: The y-intercept is the point at which the graph intersects the y-axis, while the x-intercept is the point at which the graph intersects the x-axis. The x-intercept is found by substituting y = 0 into the equation and solving for x.

Q: Can the y-intercept be a fraction?

A: Yes, the y-intercept can be a fraction. In fact, the y-intercept can be any real number, including fractions.

Q: Can the y-intercept be a decimal?

A: Yes, the y-intercept can be a decimal. In fact, the y-intercept can be any real number, including decimals.

Q: How do I graph a linear equation with a given y-intercept?

A: To graph a linear equation with a given y-intercept, use the y-intercept as the starting point and then draw a line through it with the given slope.