Question

Fill in the missing information in the chart

y = 4x - 2 _____ _____
______ 3 (0, -2)

Answer 1

To fill in the missing information in the chart for the linear equation \( y = 4x - 2 \), we can derive several points by plugging in values for \( x \).

1. **Find \( y \) when \( x = 3 \)**:
\[
y = 4(3) - 2 = 12 - 2 = 10
\]
Thus, the point when \( x = 3 \) is \( (3, 10) \).

Now, we have one completed entry in the chart:
- For \( x = 3 \), \( y = 10 \), which gives us the point \( (3, 10) \).

2. **Find another \( x \) value**. Let's plug in \( x = 0 \):
\[
y = 4(0) - 2 = -2
\]
Thus, the point when \( x = 0 \) is already given as \( (0, -2) \).

Now let's fill in the chart:

| \( x \) | \( y \) |
|---------|---------------|
| _____ | _____ |
| 3 | 10 |
| 0 | -2 |

3. Now, we need to determine another \( x \) value and find its corresponding \( y \). We can choose \( x = 1 \) for this purpose:
\[
y = 4(1) - 2 = 4 - 2 = 2
\]
Thus, we can add the point \( (1, 2) \).

Now we fill the completed chart as follows:

| \( x \) | \( y \) |
|---------|------------|
| 1 | 2 |
| 3 | 10 |
| 0 | -2 |

So, the missing numbers you can fill in are \( x = 1 \) and \( y = 2 \) for the first row.