Find The $y$-intercept Of The Line $y + 11 = -2(x - 11$\].Write Your Answer As An Integer Or As A Simplified Proper Or Improper Fraction, Not As An Ordered Pair. $\square$

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Understanding the $y$-intercept

The $y$-intercept of a linear equation is the point at which the line crosses the $y$-axis. It is the value of $y$ when $x$ is equal to zero. In other words, it is the value of $y$ that the line reaches when it intersects the $y$-axis.

The Given Equation

The given equation is $y + 11 = -2(x - 11)$. To find the $y$-intercept, we need to isolate the variable $y$ and find its value when $x$ is equal to zero.

Step 1: Simplify the Equation

To simplify the equation, we can start by distributing the negative sign to the terms inside the parentheses.

y + 11 = -2x + 22

Step 2: Isolate the Variable $y$

Next, we can isolate the variable $y$ by subtracting 11 from both sides of the equation.

y = -2x + 22 - 11

Step 3: Simplify the Equation

Now, we can simplify the equation by combining like terms.

y = -2x + 11

Step 4: Find the $y$-intercept

To find the $y$-intercept, we need to substitute $x = 0$ into the equation.

y = -2(0) + 11

Step 5: Simplify the Equation

Now, we can simplify the equation by evaluating the expression.

y = 11

Conclusion

The $y$-intercept of the line $y + 11 = -2(x - 11)$ is 11. This means that when the line intersects the $y$-axis, the value of $y$ is 11.

Example Use Case

Finding the $y$-intercept of a linear equation is an important concept in mathematics and has many practical applications. For example, in physics, the $y$-intercept of a linear equation can represent the initial velocity of an object. In economics, the $y$-intercept of a linear equation can represent the initial cost of a product.

Tips and Tricks

• When finding the $y$-intercept of a linear equation, make sure to isolate the variable $y$ and substitute $x = 0$ into the equation.
• Use the distributive property to simplify the equation and combine like terms.
• Evaluate the expression to find the value of $y$.

Common Mistakes

• Failing to isolate the variable $y$ and substitute $x = 0$ into the equation.
• Not using the distributive property to simplify the equation and combine like terms.
• Not evaluating the expression to find the value of $y$.

Conclusion

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

A: The $y$-intercept of a linear equation is the point at which the line crosses the $y$-axis. It is the value of $y$ when $x$ is equal to zero.

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

A: To find the $y$-intercept of a linear equation, you need to isolate the variable $y$ and substitute $x = 0$ into the equation.

Q: What is the first step in finding the $y$-intercept of a linear equation?

A: The first step in finding the $y$-intercept of a linear equation is to simplify the equation by distributing the negative sign to the terms inside the parentheses.

Q: How do I simplify the equation?

A: To simplify the equation, you can combine like terms and evaluate the expression.

Q: What is the final step in finding the $y$-intercept of a linear equation?

A: The final step in finding the $y$-intercept of a linear equation is to evaluate the expression and find the value of $y$.

Q: What are some common mistakes to avoid when finding the $y$-intercept of a linear equation?

A: Some common mistakes to avoid when finding the $y$-intercept of a linear equation include failing to isolate the variable $y$, not using the distributive property to simplify the equation, and not evaluating the expression to find the value of $y$.

Q: How do I use the $y$-intercept of a linear equation in real-world applications?

A: The $y$-intercept of a linear equation can be used to represent the initial velocity of an object in physics, the initial cost of a product in economics, and many other real-world applications.

Q: What are some tips and tricks for finding the $y$-intercept of a linear equation?

A: Some tips and tricks for finding the $y$-intercept of a linear equation include using the distributive property to simplify the equation, combining like terms, and evaluating the expression to find the value of $y$.

Q: Can I find the $y$-intercept of a linear equation with a variable in the numerator?

A: Yes, you can find the $y$-intercept of a linear equation with a variable in the numerator by isolating the variable $y$ and substituting $x = 0$ into the equation.

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

A: To find the $y$-intercept of a linear equation with a fraction, you need to simplify the fraction and isolate the variable $y$ before substituting $x = 0$ into the equation.

Q: Can I find the $y$-intercept of a linear equation with a negative coefficient?

A: Yes, you can find the $y$-intercept of a linear equation with a negative coefficient by isolating the variable $y$ and substituting $x = 0$ into the equation.

Conclusion

Finding the $y$-intercept of a linear equation is an important concept in mathematics that has many practical applications. By following the steps outlined in this article and avoiding common mistakes, you can find the $y$-intercept of any linear equation. Remember to isolate the variable $y$, substitute $x = 0$ into the equation, and evaluate the expression to find the value of $y$.