https://file.aiquickdraw.com/mathbot/file/1728790228421uyq3ivxh.jpg

Let's break down the problem step by step.

Given information:
- The rate of change of \( y \) with respect to \( x \) is 5, meaning \( \Delta y = 5 \cdot \Delta x \).
- When \( x = 2 \), \( y = -4 \).

### a. If \( x \) varies from \( x = 2 \) to \( x = 6 \), the change in \( x \) is:
\[
\Delta x = 6 - 2 = 4
\]

### b. If \( x \) varies from \( x = 2 \) to \( x = 6 \), the change in \( y \) is:
Since \( \Delta y = 5 \cdot \Delta x \) and \( \Delta x = 4 \),
\[
\Delta y = 5 \cdot 4 = 20
\]

### c. What is the value of \( y \) when \( x = 6 \)?
We know that the change in \( y \) from \( x = 2 \) to \( x = 6 \) is 20, and at \( x = 2 \), \( y = -4 \).

So,
\[
y = -4 + 20 = 16
\]

Thus, when \( x = 6 \), \( y = 16 \).

Let me know if you'd like further clarification on any part!

### Related questions:
1. What would be the value of \( y \) when \( x = 8 \)?
2. How do you find the slope of the function given a constant rate of change?
3. What is the general equation of a line with a constant slope?
4. How can you check if a function is linear using its rate of change?
5. How do you compute the change in \( y \) for different values of \( \Delta x \)?

**Tip:** Always remember that the rate of change, or slope, in linear equations can be interpreted as the "rise" over the "run."

y varies at a constant rate of change of 5 with respect to x, and when x = 2, y = −4. If x varies from 2 to 6, find the change in x, the change in y, and the value of y when x = 6.

Solve a linear equation where y varies at a constant rate of change of 5 with respect to x. Calculate the change in y and determine the value of y when x = 6, given that y = -4 when x = 2. This problem is suitable for Grades 7-9 students.

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