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To graph the line given by the equation \( y = -\frac{1}{3}x + 4 \), we can follow these steps:

### Step 1: Identify the slope and y-intercept.
The equation is in the slope-intercept form \( y = mx + b \), where:
- \( m \) is the slope of the line,
- \( b \) is the y-intercept (the value of \( y \) when \( x = 0 \)).

For the equation \( y = -\frac{1}{3}x + 4 \):
- The slope \( m = -\frac{1}{3} \),
- The y-intercept \( b = 4 \).

### Step 2: Plot the y-intercept.
The y-intercept is the point where the line crosses the y-axis. Since \( b = 4 \), the line will cross the y-axis at the point \( (0, 4) \). Mark this point on the graph.

### Step 3: Use the slope to find another point.
The slope is \( -\frac{1}{3} \), which means for every 3 units you move to the right (positive direction along the x-axis), you move 1 unit down (negative direction along the y-axis).

From the point \( (0, 4) \), move 3 units to the right (to \( x = 3 \)) and 1 unit down (to \( y = 3 \)). This gives the point \( (3, 3) \). Mark this point.

### Step 4: Draw the line.
Now that you have two points, \( (0, 4) \) and \( (3, 3) \), draw a straight line through these points, extending it in both directions.

This will be the graph of the line \( y = -\frac{1}{3}x + 4 \).

Would you like further details or any clarifications?

Here are 5 related questions for practice:
1. How would the graph change if the slope was \( \frac{1}{3} \) instead of \( -\frac{1}{3} \)?
2. What happens to the graph if the y-intercept is changed to 2?
3. How do you determine the slope from a graph if only the points are given?
4. What is the equation of a line parallel to this one but passing through \( (2, -1) \)?
5. How would you write the equation of a line with slope 2 and y-intercept -3?

**Tip:** Remember, the slope tells you how steep the line is and the direction it moves (up or down).

Graph the line with the equation y = -1/3x + 4.

Learn how to graph the linear equation y = -1/3x + 4. This lesson covers key algebraic concepts such as slope and y-intercept. Suitable for students in Grades 7-9.

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