In this graph, we are tasked with finding the slope, y-intercept, and equation of the line.

1. Finding the Slope:

The slope of a line is given by the formula: $m = \frac{\text{change in } y}{\text{change in } x} = \frac{y_2 - y_1}{x_2 - x_1}$ From the graph, we can identify two points on the line. Let's say the points are:

• $(0, 2)$ where the line intersects the y-axis.
• $(4, -2)$ another point on the line.

Now, apply the slope formula: $m = \frac{-2 - 2}{4 - 0} = \frac{-4}{4} = -1$ So, the slope (m) is -1.

2. Finding the Y-intercept:

The y-intercept is the point where the line crosses the y-axis. From the graph, it's clear that the line crosses the y-axis at $(0, 2)$. Thus, the y-intercept is $2$.

3. Finding the Equation:

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

Substituting the values: $y = -1x + 2 \quad \text{or} \quad y = -x + 2$ Thus, the equation of the line is: $y = -x + 2$

Summary:

• Slope (m): $-1$
• Y-intercept (b): $2$
• Equation: $y = -x + 2$

Would you like more details or have any questions about this? Here are 5 related questions to help expand on this:

1. How do you calculate the slope if given two arbitrary points?
2. What does the slope of $-1$ indicate about the line's steepness and direction?
3. How would you find the x-intercept of this line?
4. Can you convert the equation $y = -x + 2$ into standard form?
5. How does the graph of this line change if the slope or y-intercept were different?

Tip: When plotting a line from an equation, start by plotting the y-intercept, then use the slope to find another point.