Absolutely! We need to graph the linear function [tex]\( f(x) = -\frac{1}{3}x + 8 \)[/tex]. Let's go through the detailed steps required.
1. Identify the y-intercept: The y-intercept of a linear equation in the form [tex]\( y = mx + b \)[/tex] is [tex]\( b \)[/tex]. Here, [tex]\( b = 8 \)[/tex]. So, the y-intercept is at the point (0, 8).
2. Plot the y-intercept: On the graph, plot the point (0, 8).
3. Identify the slope: The slope [tex]\( m \)[/tex] of the line is [tex]\(-\frac{1}{3} \)[/tex]. This indicates that for every 3 units you move to the right along the x-axis, you move 1 unit down along the y-axis, since the slope is negative.
4. Use the slope to find another point:
- Start from the y-intercept (0, 8).
- Move 3 units to the right (positive direction on the x-axis).
- Move 1 unit down (negative direction on the y-axis, due to the negative sign of the slope).
This gives us the point (3, 7) as another point on the line.
5. Plot the second point: On the graph, plot the point (3, 7).
6. Draw the line: Use a ruler or the line drawing tool to connect the points (0, 8) and (3, 7) with a straight line. Extend this line through both points across the graph to accurately represent the linear function.
With these steps, you have successfully graphed the function [tex]\( f(x) = -\frac{1}{3}x + 8 \)[/tex]. The line should extend infinitely in both directions but typically gets cut off based on the graphing area you are working within.
To summarize:
- Y-intercept is at (0, 8)
- Another point using the slope is at (3, 7)
- Draw a line through these points to represent the equation.
Your graph will show a downward-sloping line from left to right due to the negative slope.
