The problem shown in the image asks for the equation of the line represented on the graph. Let's go through the steps to find the equation of this line.

Step 1: Identify Two Points on the Line

From the graph, the line passes through two clear points:

• Point 1: $(0, 2)$
• Point 2: $(3, 0)$

Step 2: Calculate the Slope (m)

The slope $m$ of a line is given by the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Using the points $(0, 2)$ and $(3, 0)$, we can substitute: $m = \frac{0 - 2}{3 - 0} = \frac{-2}{3}$ Thus, the slope $m = -\frac{2}{3}$.

Step 3: Use the Slope-Intercept Form

The equation of a line in slope-intercept form is: $y = mx + b$ We already know $m = -\frac{2}{3}$, and we can use the point $(0, 2)$, where the line crosses the y-axis, to find $b$, the y-intercept.

Since the y-intercept is the point where $x = 0$, we can see that $b = 2$.

Final Equation

Substituting $m = -\frac{2}{3}$ and $b = 2$ into the slope-intercept form: $y = -\frac{2}{3}x + 2$

So, the equation of the line is: $\boxed{y = -\frac{2}{3}x + 2}$

Let me know if you need any clarifications or further details.

Questions to Explore:

1. What is the slope of a horizontal line?
2. How does changing the slope affect the steepness of a line?
3. What happens to the equation of a line if the slope is zero?
4. How can you find the slope of a line given only its graph?
5. Can a line have a positive y-intercept and a negative slope?

Tip: Always use two clear points to calculate the slope to avoid mistakes!