Graph y=-3x-1, using a table of values. (Use values other than 0 and 1 as a value for x)



To graph the equation \( y = -3x - 1 \), we can create a table of values by selecting a few values for \( x \), calculating the corresponding \( y \)-values, and then plotting the points on the coordinate plane.

### Step-by-Step:

1. **Select values for \( x \)**: Choose values that are easy to calculate. For this example, let's use \( x = -2 \), \( x = -1 \), \( x = 2 \), and \( x = 3 \).

2. **Calculate corresponding \( y \)-values**: Substitute each \( x \)-value into the equation \( y = -3x - 1 \).

| \( x \) | Calculation for \( y \)          | \( y \)-value |
|--------|-----------------------------------|---------------|
| \( -2 \) | \( y = -3(-2) - 1 = 6 - 1 \)     | \( y = 5 \)   |
| \( -1 \) | \( y = -3(-1) - 1 = 3 - 1 \)     | \( y = 2 \)   |
| \( 2 \)  | \( y = -3(2) - 1 = -6 - 1 \)     | \( y = -7 \)  |
| \( 3 \)  | \( y = -3(3) - 1 = -9 - 1 \)     | \( y = -10 \) |

Now we have the following points:
\[
(-2, 5), (-1, 2), (2, -7), (3, -10)
\]

### Table of Values:

| \( x \)  | \( y \) |
|----------|---------|
| -2       | 5       |
| -1       | 2       |
| 2        | -7      |
| 3        | -10     |

### Graph:
Plot these points on the graph and draw a straight line through them, as the equation represents a linear function.

Would you like a graph for this, or have any questions?

### 5 Follow-up Questions:
1. How does the slope of the line affect the steepness of the graph?
2. What happens to the graph if we change the slope to a positive value?
3. How would you find the intercepts of this line?
4. Can you explain how to determine the slope from the equation \( y = -3x - 1 \)?
5. What would the graph look like if the equation were \( y = -3x + 1 \)?

### Tip:
When graphing lines, always try to choose both positive and negative values for \( x \) to get a clearer picture of the line's behavior!

Graph y=-3x-1, using a table of values. (Use values other than 0 and 1 as a value for x)

Learn how to graph the linear equation y = -3x - 1 using a table of values. This problem covers key algebraic concepts, such as graphing linear equations and understanding the slope-intercept form. Suitable for students in Grades 7-9.

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