https://file.aiquickdraw.com/mathbot/file/17260375428611cc1y7m0.jpg

The problem in the image is asking to express \( y \) in terms of \( z \) from the given formula:

\[
2 - \frac{1}{y} = z
\]

Let's solve for \( y \) step by step:

1. Start with the equation:
   \[
   2 - \frac{1}{y} = z
   \]

2. Subtract 2 from both sides:
   \[
   -\frac{1}{y} = z - 2
   \]

3. Multiply both sides by -1 to isolate the fraction:
   \[
   \frac{1}{y} = 2 - z
   \]

4. Take the reciprocal of both sides to solve for \( y \):
   \[
   y = \frac{1}{2 - z}
   \]

Thus, the correct expression for \( y \) in terms of \( z \) is:

\[
y = \frac{1}{2 - z}
\]

Looking at the options, the correct one is **B.**

Let me know if you'd like further explanation or have more questions!

Here are 5 related questions for deeper practice:
1. How would the formula change if the initial equation were \( 2 - \frac{2}{y} = z \)?
2. What would be the value of \( y \) if \( z = 1 \)?
3. Can you find the inverse of the function \( y = \frac{1}{2 - z} \)?
4. How does the expression for \( y \) change if you add 3 to both sides of the original equation?
5. How would the formula look if the denominator were \( z + 2 \) instead?

**Tip:** Always check if you can isolate a variable by performing basic arithmetic operations (addition, subtraction, multiplication, or division) before applying more complex steps like taking reciprocals.

З формули 2 - 1/y = z виразіть змінну y через z.

Learn how to solve the equation 2 - 1/y = z to express y in terms of z. This problem demonstrates essential algebraic techniques like equation manipulation and reciprocal functions, ideal for students in Grades 9-11.

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