To determine the slope and $y$-intercept of the line from the image:

1. Find two points on the line:
   The line clearly passes through the points $(0, 2)$ and $(4, 6)$.

2. Calculate the slope ($m$) using the slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting $(x_1, y_1) = (0, 2)$ and $(x_2, y_2) = (4, 6)$: $m = \frac{6 - 2}{4 - 0} = \frac{4}{4} = 1$ The slope is $m = 1$.

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

Final Answer:

• Slope ($m$): $1$
• $y$-intercept ($b$): $2$

Would you like further clarification or help with similar problems?

Related Questions:

1. What does the slope represent in real-world situations?
2. How do you write the equation of a line using the slope-intercept form?
3. Can a line have no $y$-intercept? Why or why not?
4. How do parallel lines compare in terms of slope?
5. How would you calculate the slope if one of the coordinates was negative?

Tip:

The slope-intercept form of a line is $y = mx + b$. Use this to quickly write equations of lines once you know the slope and intercept!