Question

Fill in the table and graph the following linear equation
y = 1/4x-3
[Table] X Y
-4 {blank}
-2 {blank}
0 {blank}
4 {blank}
The graph has a horizontal of 5 units and a vertical of 5 units, and has 4 quadrants.

Answer 1

To fill in the table for the linear equation \( y = \frac{1}{4}x - 3 \), we will calculate the value of \( y \) for each given \( x \).

### Calculations

1. **For \( x = -4 \)**:
\[
y = \frac{1}{4}(-4) - 3 = -1 - 3 = -4
\]

2. **For \( x = -2 \)**:
\[
y = \frac{1}{4}(-2) - 3 = -\frac{1}{2} - 3 = -\frac{1}{2} - \frac{6}{2} = -\frac{7}{2} = -3.5
\]

3. **For \( x = 0 \)**:
\[
y = \frac{1}{4}(0) - 3 = 0 - 3 = -3
\]

4. **For \( x = 4 \)**:
\[
y = \frac{1}{4}(4) - 3 = 1 - 3 = -2
\]

### Completed Table

Now, let's summarize the values in the table:

| X | Y |
|-----|-------|
| -4 | -4 |
| -2 | -3.5 |
| 0 | -3 |
| 4 | -2 |

### Graphing the Linear Equation

To graph the line \( y = \frac{1}{4}x - 3 \):

1. **Plot the points** from the table:
- Point (-4, -4)
- Point (-2, -3.5)
- Point (0, -3)
- Point (4, -2)

2. **Draw the line** through the points.

### Graphing Instructions
Given that your graph has a horizontal scale of 5 units and a vertical scale of 5 units, you can add appropriate labels along the axes to accommodate the points you calculated. Make sure the four quadrants are represented, with the considering the negative values for \( y \), especially for the plotted points.

The slope of \( \frac{1}{4} \) indicates that for every 4 units you move horizontally to the right (increasing \( x \)), the \( y \) value increases by 1 unit, hence depicting a gentle upward slope.

If you are drawing on graph paper or using graphing software, ensure that the axes extend adequately to display your specified points from the table.

### Final Thoughts
You can now create a clear graph representing the linear equation with the points plotted, resulting in a straight line as indicated by the equation.