Let's solve the problem step by step based on the given graph:

1. Find the Slope

The slope ($m$) of a line is calculated as: $m = \frac{\text{rise}}{\text{run}}$

Looking at the graph:

• Take two clear points on the line, e.g., $(-4, -2)$ and $(2, 4)$.
• Calculate the rise (change in $y$): $4 - (-2) = 6$.
• Calculate the run (change in $x$): $2 - (-4) = 6$.

Thus, the slope is: $m = \frac{6}{6} = 1$

2. Identify the y-Intercept

The $y$-intercept ($b$) is the point where the line crosses the $y$-axis. From the graph, the line crosses the $y$-axis at $y = 2$. Therefore, the $y$-intercept is: $(0, 2)$

3. Write the Equation of the Line

The slope-intercept form of a line is: $y = mx + b$

Substitute $m = 1$ and $b = 2$: $y = 1x + 2 \quad \text{or simply} \quad y = x + 2$

Final Answers:

1. Slope: $1$
2. y-Intercept: $(0, 2)$
3. Equation: $y = x + 2$

Would you like further explanation on any of these steps? Here are some related questions to explore:

1. What does a slope of $1$ signify geometrically?
2. How do you calculate slope with negative coordinates?
3. Can you identify other points on this line using its equation?
4. How does changing the $y$-intercept affect the graph?
5. What happens to the equation if the slope is steeper (e.g., $m = 2$)?

Tip: Always verify your slope and intercept by checking with at least two points from the graph!