The equation given in the image is in slope-intercept form:

$y = -\frac{8}{3}x + 3$

This equation follows the form $y = mx + b$, where:

• $m$ is the slope of the line (here, $m = -\frac{8}{3}$),
• $b$ is the y-intercept (here, $b = 3$).

Step-by-step Graphing Instructions:

1. Plot the y-intercept: The y-intercept is $b = 3$. So, plot a point at (0, 3) on the y-axis.

2. Use the slope: The slope is $-\frac{8}{3}$, meaning for every 3 units you move to the right along the x-axis, move 8 units down (since the slope is negative). From the point (0, 3), move:

   • 3 units to the right (positive direction on the x-axis),
   • 8 units down (since the slope is negative).

   This leads to the point (3, -5).

3. Draw the line: Now, connect the two points (0, 3) and (3, -5) with a straight line.

The graph should show a downward sloping line passing through these points.

Let me know if you'd like to see the graph or need more details!

Here are five related questions:

1. How do you find the slope from two points on a line?
2. What is the significance of the y-intercept in real-life problems?
3. How would you graph a line with a positive slope?
4. What happens to the graph if the slope becomes zero?
5. How do you convert from standard form to slope-intercept form?

Tip: When plotting lines, always remember to check the scale on both the x and y axes to ensure accuracy.