if x is directly proportional to y and x1=160, y1=4 and x2=200 then find y2

Given that \( x \) is directly proportional to \( y \), we can express this relationship as:

\[
x = k \cdot y
\]

Where \( k \) is the constant of proportionality. To solve for \( y_2 \), follow these steps:

### Step 1: Find the constant \( k \)
Using the values of \( x_1 = 160 \) and \( y_1 = 4 \):

\[
k = \frac{x_1}{y_1} = \frac{160}{4} = 40
\]

### Step 2: Use \( k \) to find \( y_2 \)
Now, with \( x_2 = 200 \) and \( k = 40 \), we can find \( y_2 \) using the same proportional relationship:

\[
y_2 = \frac{x_2}{k} = \frac{200}{40} = 5
\]

Thus, \( y_2 = 5 \).

Do you need further details or have any questions?

Here are 5 related questions:
1. How is the constant of proportionality determined in direct proportionality?
2. What changes if the relationship is inverse proportionality?
3. Can direct proportionality apply to more complex functions, like quadratic?
4. How do you solve problems where both variables change non-linearly?
5. What real-life examples involve direct proportionality?

**Tip:** In direct proportionality, as one variable increases, the other increases at the same rate due to the constant ratio.

If x is directly proportional to y and x1=160, y1=4 and x2=200 then find y2.

Solve the problem where x is directly proportional to y, with x1=160, y1=4, and x2=200. Learn how to determine the constant of proportionality and use it to find y2. This solution is suitable for students in Grades 6-8 and covers key algebra concepts like direct proportionality.

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