https://file.aiquickdraw.com/mathbot/file/1728064125034z2p84ik7.jpg

The image you've uploaded contains a linear equation \( y = 3x - 1 \), a table with columns for \( x \) and \( y \), and a graph with axes prepared for plotting points.

Here’s how we can proceed:

### Step 1: Fill the table
We will substitute different values for \( x \) into the equation \( y = 3x - 1 \) and compute the corresponding values of \( y \).

1. If \( x = -1 \):
   \[
   y = 3(-1) - 1 = -3 - 1 = -4
   \]
   So, \( (-1, -4) \) is one point.

2. If \( x = 0 \):
   \[
   y = 3(0) - 1 = 0 - 1 = -1
   \]
   So, \( (0, -1) \) is another point.

3. If \( x = 1 \):
   \[
   y = 3(1) - 1 = 3 - 1 = 2
   \]
   So, \( (1, 2) \) is another point.

4. If \( x = 2 \):
   \[
   y = 3(2) - 1 = 6 - 1 = 5
   \]
   So, \( (2, 5) \) is another point.

The table would be:
\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-1 & -4 \\
0 & -1 \\
1 & 2 \\
2 & 5 \\
\hline
\end{array}
\]

### Step 2: Plot the points on the graph
Now, using the points \((-1, -4)\), \( (0, -1) \), \( (1, 2) \), and \( (2, 5)\), you can plot them on the graph. After plotting, connect the points to form a straight line, since the equation is linear.

Would you like more details on how to plot the points, or do you have any other questions?

Here are 5 questions related to this concept:

1. What is the slope of the line represented by the equation \( y = 3x - 1 \)?
2. How does the slope affect the steepness of the line?
3. What is the y-intercept in the equation \( y = 3x - 1 \), and how can we find it?
4. How do we know that this equation represents a linear function?
5. What would happen to the graph if the equation were \( y = -3x - 1 \)?

**Tip:** When graphing a linear equation, always start by plotting the y-intercept and use the slope to find other points.

Fill in the table and graph the equation y = 3x - 1.

Learn how to fill in a table and graph the linear equation y = 3x - 1. This tutorial covers core algebra concepts, including the slope-intercept form and graphing techniques. Suitable for students in Grades 7-9.

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