Let's solve the problem based on the graph in the image.

Step 1: Determine the slope.

To find the slope, use two points from the line. From the graph, two points that lie on the line are approximately:

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

The slope formula is given by: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting the values of the points: $m = \frac{-1 - 2}{2 - (-1)} = \frac{-3}{3} = -1$ So, the slope $m = -1$.

Step 2: Find the y-intercept.

The y-intercept occurs where the line crosses the y-axis. From the graph, we can see that the line crosses the y-axis at $(0, 1)$. Therefore, the y-intercept is $1$.

Step 3: Write the equation of the line.

Using the slope-intercept form of a line: $y = mx + b$ where $m$ is the slope and $b$ is the y-intercept, we can substitute the values: $y = -x + 1$

Final Answer:

• Slope = $-1$
• y-intercept = $1$
• Equation: $y = -x + 1$

Do you want more details or have any other questions?

Here are 5 related questions to explore:

1. How do you find the slope if the points are not clear?
2. Can a line have a slope of zero? What would its equation look like?
3. What if the line passed through the origin (0,0)? How would that affect the equation?
4. How do you determine the x-intercept from a line equation?
5. What is the significance of the slope in real-world problems?

Tip: When calculating slope, remember that a positive slope means the line is rising, and a negative slope means the line is falling as you move from left to right.