The function given in the image is:

$f(x) = -\frac{8}{9}x$

This is a linear function of the form $f(x) = mx + b$, where:

• $m = -\frac{8}{9}$ is the slope of the line.
• $b = 0$, meaning the y-intercept is at the origin (0, 0).

Steps to graph the function:

1. Plot the y-intercept: Since $b = 0$, the line passes through the origin (0, 0).

2. Use the slope: The slope $m = -\frac{8}{9}$ tells us how to move between points on the line. The slope means for every 9 units you move to the right (positive direction on the x-axis), you move 8 units down (negative direction on the y-axis).

   • From the origin, go right 9 units to (9, 0), and then go down 8 units to (9, -8). This gives you the point (9, -8).
   • You can also plot points in the opposite direction: go left 9 units (negative direction on the x-axis), and up 8 units. This will give you the point (-9, 8).

3. Draw the line: Once you have these points, draw a straight line through them. This is the graph of the function.

Looking at the graph in the image, it appears to follow this pattern correctly. The line passes through (0, 0) and has a slope that moves down as it progresses to the right, consistent with $m = -\frac{8}{9}$.

Would you like a further breakdown of how to interpret or verify slope and intercepts?

Here are 5 related questions you might consider:

1. What happens to the graph if the slope changes to $m = \frac{8}{9}$?
2. How would the graph shift if the y-intercept was $b = 2$?
3. How do you find the slope between two points on a line?
4. What does a slope of 0 represent in a graph?
5. How do you graph a line if it is written in point-slope form instead of slope-intercept form?

Tip: Always start plotting with the y-intercept, as it gives you an anchor point for the entire graph.