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The problem involves filling in the table using the equation \( y = 3.2x + 5 \), and then checking whether \( y \) is proportional to \( x \). Let's go through the steps:

### 1. Filling in the table

We are given the equation:
\[
y = 3.2x + 5
\]
Now we will compute the values for \( y \) for different values of \( x \).

- When \( x = 1 \):
\[
y = 3.2(1) + 5 = 3.2 + 5 = 8.2
\]

- When \( x = 2 \):
\[
y = 3.2(2) + 5 = 6.4 + 5 = 11.4
\]

- When \( x = 4 \):
\[
y = 3.2(4) + 5 = 12.8 + 5 = 17.8
\]

So, the table should be filled in as follows:

\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
1 & 8.2 \\
2 & 11.4 \\
4 & 17.8 \\
\hline
\end{array}
\]

### 2. Is \( y \) proportional to \( x \)?

Two variables are proportional if they have a constant ratio. That is, if \( y = kx \) for some constant \( k \), then \( y \) is proportional to \( x \).

In this case, the equation is \( y = 3.2x + 5 \), which includes the additional constant \( +5 \). This means that \( y \) is not proportional to \( x \), because there is no constant ratio. The constant term \( +5 \) breaks the proportional relationship.

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### Related Questions:
1. What is the formula for checking if two variables are proportional?
2. How do you find the slope in a linear equation like \( y = 3.2x + 5 \)?
3. Can you identify the intercept in the equation \( y = 3.2x + 5 \)?
4. What is the difference between proportional and non-proportional relationships?
5. How would you graph this linear equation?

**Tip:** If there is an additional constant added or subtracted in a linear equation, the relationship is not proportional.

Use the equation y = 3.2x + 5 to fill in the table. Is y proportional to x? Explain why or why not.

Solve the linear equation y = 3.2x + 5 and determine whether y is proportional to x. Learn key concepts of proportionality and the slope-intercept form. Suitable for students in Grades 8-10.

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