Let's analyze the graph to find the requested information: slope, y-intercept, and the equation.

Slope:

The line passes through two points that I can identify:

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

Using the slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are the coordinates of two points on the line: $m = \frac{-2 - 1}{3 - 0} = \frac{-3}{3} = -1$ So, the slope is $-1$.

Y-Intercept:

The y-intercept is the point where the line crosses the y-axis. From the graph, the line crosses the y-axis at $(0, 1)$. Therefore, the y-intercept is $1$.

Equation:

Using the slope-intercept form of a linear equation, $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept: $y = -x + 1$

Summary:

• Slope: $-1$
• Y-Intercept: $1$
• Equation: $y = -x + 1$

Would you like more details or further clarifications?

Here are 5 related questions to expand on this:

1. How do you calculate the slope from any two points on a line?
2. What does a negative slope indicate about the direction of a line?
3. How can you find the x-intercept from an equation in slope-intercept form?
4. What is the relationship between slope and rate of change in real-world applications?
5. How does the y-intercept affect the position of a line on a graph?

Tip: The slope-intercept form $y = mx + b$ is very useful for quickly graphing a line, as $m$ gives the steepness and direction, and $b$ gives the starting point on the y-axis.