Question

Graph this line using the slope and y-intercept:
y=
1/
3
x–8

1-8 x and y axis

Answer 1

To graph the line given by the equation \( y = \frac{1}{3}x - 8 \), we can identify the slope and y-intercept first.

### Step 1: Identify the y-intercept
The y-intercept is the point where the line crosses the y-axis (where \( x = 0 \)). From the equation:

\[
y = \frac{1}{3}(0) - 8
\]
\[
y = -8
\]

So the y-intercept is at the point (0, -8).

### Step 2: Identify the slope
The slope of the line is given by the coefficient of \( x \), which is \( \frac{1}{3} \). This means that for every 1 unit increase in \( x \), \( y \) increases by \( \frac{1}{3} \).

### Step 3: Plotting points
1. **Start at the y-intercept (0, -8)** on the graph.
2. **Use the slope** to find another point. Starting from (0, -8), if you move 3 units to the right (positive x-direction), you move up 1 unit (positive y-direction):
- From (0, -8) to (3, -7) (up 1 from -8)
3. You can plot additional points by continuing from (3, -7). Move another 3 units to the right and 1 unit up:
- From (3, -7) to (6, -6) (up 1 from -7)

### Step 4: Graph the line
Once you have plotted these points (0, -8), (3, -7), and (6, -6), you can draw a straight line through these points.

### Visualization
The line will rise gently from the left to right due to a positive slope of \( \frac{1}{3} \).

### Final Note
If your graphing plane includes limits within (-8, 1) on the y-axis, make sure your graph extends far enough to include the points you plotted. The line will continue indefinitely in both the positive and negative directions beyond the points you plotted.