Question

or
Graph this line using the slope and y-intercept:
y=
1
3
x+8
Click to select points on the graph.

Answer 1

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

1. **Identify the slope and y-intercept:**
- The slope (\( m \)) is \( \frac{1}{3} \).
- The y-intercept (\( b \)) is \( 8 \). This means the line crosses the y-axis at the point \( (0, 8) \).

2. **Plot the y-intercept:**
- Start by plotting the point \( (0, 8) \) on the graph.

3. **Use the slope to find another point:**
- The slope \( \frac{1}{3} \) means that for every 3 units you move to the right (positive x-direction), you move up 1 unit (positive y-direction).
- From the point \( (0, 8) \):
- Move 3 units right to \( (3, 8) \) and then move up 1 unit to \( (3, 9) \). Plot the point \( (3, 9) \).

4. **Draw the line:**
- Connect the points \( (0, 8) \) and \( (3, 9) \) with a straight line. Extend the line in both directions.

This defines the line representing the equation \( y = \frac{1}{3}x + 8 \).

If you have access to graphing tools, you can also input this equation directly into a graphing calculator or software to visualize the line. If you want to select specific points on a generated graph, you could choose points like \( (0, 8) \), \( (3, 9) \), \( (6, 10) \) (moving right 3 more units and up 1 more unit from \( (3, 9) \)), etc.