Determine The \[$ Y \$\]-intercept Of The Following Equation.$\[ (-x-2)(x-4)=y \\]Answer Choices:A. \[$ (0, -8) \$\] B. \[$ (0, 8) \$\] C. \[$ (2, 0) \$\] And \[$ (4, 0) \$\] D. \[$ (8, 0)

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Understanding the y-intercept

The y-intercept of a linear equation is the point at which the graph of the equation intersects the y-axis. In other words, it is the value of y when x is equal to zero. To determine the y-intercept of a given equation, we need to substitute x = 0 into the equation and solve for y.

Given Equation

The given equation is (−x−2)(x−4)=y{(-x-2)(x-4)=y}. Our goal is to determine the y-intercept of this equation, which means we need to find the value of y when x = 0.

Step 1: Substitute x = 0 into the Equation

To find the y-intercept, we need to substitute x = 0 into the given equation. This will give us an equation in terms of y only.

(−0−2)(0−4)=y{(-0-2)(0-4)=y}

Simplifying the equation, we get:

(−2)(−4)=y{(-2)(-4)=y}

Step 2: Simplify the Equation

Now, we need to simplify the equation to find the value of y.

(−2)(−4)=y{(-2)(-4)=y}

Using the rule that a×(−b)=−ab{a \times (-b) = -ab}, we can simplify the equation as follows:

8=y{8=y}

Step 3: Write the y-intercept in the Correct Format

The y-intercept is the point at which the graph of the equation intersects the y-axis. Therefore, we need to write the y-intercept in the correct format, which is (0, y).

The y-intercept of the given equation is (0, 8).

Conclusion

In this article, we determined the y-intercept of the given equation (−x−2)(x−4)=y{(-x-2)(x-4)=y}. We substituted x = 0 into the equation, simplified it, and found that the y-intercept is (0, 8).

Answer Choice

Based on our calculation, the correct answer choice is:

B. (0, 8)

Discussion

The y-intercept is an important concept in mathematics, particularly in algebra and geometry. It is used to determine the point at which the graph of an equation intersects the y-axis. In this article, we demonstrated how to determine the y-intercept of a given equation by substituting x = 0 into the equation and simplifying it.

Related Topics

  • Linear Equations: Linear equations are equations in which the highest power of the variable is 1. They can be written in the form ax + b = c, where a, b, and c are constants.
  • Graphing Linear Equations: Graphing linear equations involves plotting the points on a coordinate plane and drawing a line through them.
  • Solving Systems of Linear Equations: Solving systems of linear equations involves finding the solution to a system of two or more linear equations.

Practice Problems

  1. Determine the y-intercept of the equation x + 2y = 4.
  2. Find the y-intercept of the equation 2x - 3y = 5.
  3. Determine the y-intercept of the equation x - 2y = -3.

Answer Key

  1. (0, 2)
  2. (0, -10/3)
  3. (0, 3/2)

Conclusion

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 of the equation intersects the y-axis. It is the value of y when x is equal to zero.

Q: How do I determine the y-intercept of a given equation?

A: To determine the y-intercept of a given equation, you need to substitute x = 0 into the equation and solve for y.

Q: What is the formula for determining the y-intercept?

A: The formula for determining the y-intercept is:

y = f(0)

where f(x) is the given equation.

Q: Can I use the y-intercept to graph a linear equation?

A: Yes, you can use the y-intercept to graph a linear equation. The y-intercept is the point at which the graph of the equation intersects the y-axis. You can use this point to draw a line through the other points on the graph.

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

A: To find the y-intercept of a quadratic equation, you need to substitute x = 0 into the equation and solve for y. The quadratic equation will be in the form ax^2 + bx + c = 0, where a, b, and c are constants.

Q: Can I use the y-intercept to solve a system of linear equations?

A: Yes, you can use the y-intercept to solve a system of linear equations. The y-intercept is the point at which the graph of one of the equations intersects the y-axis. You can use this point to find the solution to the system of equations.

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

A: The y-intercept is the point at which the graph of a linear equation intersects the y-axis, while the x-intercept is the point at which the graph of a linear equation intersects the x-axis.

Q: Can I use the y-intercept to find the slope of a linear equation?

A: No, you cannot use the y-intercept to find the slope of a linear equation. The slope of a linear equation is the ratio of the change in y to the change in x, and it is not related to the y-intercept.

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

A: To determine the y-intercept of a non-linear equation, you need to substitute x = 0 into the equation and solve for y. However, the equation may not be in the form of a linear equation, and you may need to use other methods to solve for y.

Q: Can I use the y-intercept to graph a non-linear equation?

A: Yes, you can use the y-intercept to graph a non-linear equation. However, the graph of a non-linear equation may not be a straight line, and you may need to use other methods to graph the equation.

Conclusion

In this article, we answered frequently asked questions about determining the y-intercept of a linear equation. We discussed the formula for determining the y-intercept, how to use the y-intercept to graph a linear equation, and how to find the y-intercept of a quadratic equation. We also discussed the difference between the y-intercept and the x-intercept, and how to use the y-intercept to solve a system of linear equations. Finally, we provided answers to additional questions about determining the y-intercept of a non-linear equation and graphing a non-linear equation.