To analyze the graph, let's follow these steps:

a) Slope of the line:

The slope $m$ of a line is the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

From the graph, two points on the line can be identified:

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

Now, we calculate the slope $m$: $m = \frac{\text{rise}}{\text{run}} = \frac{1 - (-1)}{0 - (-2)} = \frac{2}{2} = 1$ So, the slope of the line is $m = 1$.

b) Equation of the line in slope-intercept form:

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

• $m$ is the slope
• $b$ is the y-intercept

From the graph, the y-intercept (where the line crosses the y-axis) is $b = 1$. Thus, the equation of the line is: $y = 1x + 1$ or simply: $y = x + 1$

Summary:

• Slope of the line $m = 1$
• Equation of the line: $y = x + 1$

Would you like more details or have any questions?

Here are some related questions for further exploration:

1. What happens to the equation if the slope is negative?
2. How do you find the slope when the line is horizontal?
3. What is the equation of a line parallel to this one?
4. How can you find the slope using the angle of inclination of the line?
5. How does the slope-intercept form differ from the point-slope form?

Tip: The slope-intercept form is useful for quickly identifying the slope and y-intercept of a line!