Graph the function \( f(x)=-\frac{1}{4} x-1 \)

To graph the function \( f(x) = -\frac{1}{4} x - 1 \), we can follow these steps: 1. **Identify the slope and y-intercept**: - The function is in the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. - Here, the slope \( m = -\frac{1}{4} \) and the y-intercept \( b = -1 \). 2. **Plot the y-intercept**: - The y-intercept is the point where the graph crosses the y-axis. For this function, it is at the point \( (0, -1) \). 3. **Use the slope to find another point**: - The slope of \( -\frac{1}{4} \) means that for every 4 units you move to the right (positive direction on the x-axis), you move down 1 unit (negative direction on the y-axis). - Starting from the y-intercept \( (0, -1) \): - Move 4 units to the right to \( (4, -1) \). - Move down 1 unit to \( (4, -2) \). - So, another point on the graph is \( (4, -2) \). 4. **Plot the points**: - Plot the points \( (0, -1) \) and \( (4, -2) \) on the graph. 5. **Draw the line**: - Connect the points with a straight line, extending it in both directions. 6. **Label the axes**: - Make sure to label the x-axis and y-axis for clarity. The graph of the function \( f(x) = -\frac{1}{4} x - 1 \) will be a straight line that slopes downwards from left to right, crossing the y-axis at \( (0, -1) \). If you were to sketch it, it would look like this: ``` y | 1| . | . 0|-----. | . -1|. | -2| . |________________ x -4 -3 -2 -1 0 1 2 3 4 ``` This is a rough representation of the graph. The line continues infinitely in both directions.