Question

Graph the equation by plotting points.
yequalsone half
xminus4

Answer 1

To graph the equation \( y = \frac{1}{2}x - 4 \), we can plot points by selecting different values for \( x \) and calculating the corresponding \( y \) values.

### Step 1: Choose values for \( x \).

Let’s choose a few values for \( x \):
- \( x = -4 \)
- \( x = 0 \)
- \( x = 4 \)
- \( x = 8 \)

### Step 2: Calculate corresponding \( y \) values.

1. For \( x = -4 \):
\[
y = \frac{1}{2}(-4) - 4 = -2 - 4 = -6
\]
So, the point is \((-4, -6)\).

2. For \( x = 0 \):
\[
y = \frac{1}{2}(0) - 4 = 0 - 4 = -4
\]
So, the point is \((0, -4)\).

3. For \( x = 4 \):
\[
y = \frac{1}{2}(4) - 4 = 2 - 4 = -2
\]
So, the point is \((4, -2)\).

4. For \( x = 8 \):
\[
y = \frac{1}{2}(8) - 4 = 4 - 4 = 0
\]
So, the point is \((8, 0)\).

### Step 3: Plot the points.

Now, let's summarize the points we have:

- \((-4, -6)\)
- \((0, -4)\)
- \((4, -2)\)
- \((8, 0)\)

### Step 4: Draw the graph.

1. On graph paper or using a coordinate system, plot the points calculated above.
2. Draw a straight line through the points. The equation \( y = \frac{1}{2}x - 4 \) represents a straight line.

### Conclusion:
The slope of the line is \( \frac{1}{2} \), which means for every 2 units you move up in \( y \), you move 1 unit to the right in \( x \). The y-intercept, where the line crosses the y-axis, is \(-4\).

You should see a straight line that rises gently from left to right, crossing the y-axis at \(-4\).