https://file.aiquickdraw.com/mathbot/file/1726379882867lc2tefns.jpg

Let's work through the two questions in the image:

### First Question:
The given equation is:
\[
y = 22 + 3.9x
\]
We are asked to find the value of \(x\) when \(y = 69\).

Substitute \(y = 69\) into the equation and solve for \(x\):
\[
69 = 22 + 3.9x
\]
Subtract 22 from both sides:
\[
47 = 3.9x
\]
Now divide both sides by 3.9:
\[
x = \frac{47}{3.9}
\]
Let's compute this value.

### Second Question:
The given equation is:
\[
x = \frac{7y - 4}{4}
\]
We are asked to solve for \(y\) in terms of \(x\).

Multiply both sides of the equation by 4:
\[
4x = 7y - 4
\]
Now add 4 to both sides:
\[
4x + 4 = 7y
\]
Finally, divide by 7:
\[
y = \frac{4x + 4}{7}
\]
So, the correct answer for this question is \( \frac{4x + 4}{7} \), which corresponds to option D.

Now, let's compute the first answer.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, you can solve the first question manually by calculating:

\[
x = \frac{47}{3.9} \approx 12.05
\]

So, the correct answer for the first question is \( x \approx 12.05 \), which corresponds to option **B**.

If you have any further questions or need more help, feel free to ask! Here are some related questions:

1. What happens to \(x\) if \(y\) is increased to a higher value in the equation \( y = 22 + 3.9x \)?
2. Can you derive the relationship between \(x\) and \(y\) if the spring constant changes from 3.9 to another value?
3. How would you solve the second equation if it were written in terms of \(y\) from the beginning?
4. What is the interpretation of the constant term 22 in the equation \( y = 22 + 3.9x \)?
5. How does multiplying both sides of an equation help in solving for a specific variable?

**Tip**: When solving for a variable, isolating the variable step by step makes it easier to simplify the problem.

One end of a spring is attached to the top of the tent. When an object of mass x grams is attached to the other end of the spring, the spring stretches to a length of y inches as shown in the equation y = 22 + 3.9x. What is x when y is 69?
If x = (7y - 4) / 4, what is the value of y in terms of x?

Learn how to solve a linear equation involving spring stretch with mass x and length y, as well as solve for y in terms of x using algebra. This problem involves solving for variables and manipulating equations. Suitable for Grades 9-10 students.

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