The image shows a graph with a line crossing through a grid, along with two questions:

1. The slope of the line (select):
2. The y-intercept of the graph (select):

Let me analyze the graph to determine the slope and y-intercept.

• Y-intercept: The y-intercept is the point where the line crosses the y-axis.
• Slope: The slope can be calculated by finding two points on the line and using the formula:

$\text{slope} = \frac{\text{change in y}}{\text{change in x}} = \frac{y_2 - y_1}{x_2 - x_1}$

Let me extract this information.From the graph, we can make the following observations:

• Y-intercept: The line crosses the y-axis at $y = 2$.
• Slope: We can observe two points on the line, for example, at $(0, 2)$ and $(4, 0)$.

To find the slope, we use the formula:

$\text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 2}{4 - 0} = \frac{-2}{4} = -\frac{1}{2}$

Thus:

• The slope of the line is $-\frac{1}{2}$.
• The y-intercept is $2$.

Would you like further details, or do you have any other questions?

Here are five related questions to explore:

1. How do you calculate the slope of a line given any two points?
2. What is the significance of the y-intercept in a linear equation?
3. How can the slope of a line affect its appearance on a graph?
4. What is the formula for a line in slope-intercept form?
5. How do horizontal and vertical lines differ in terms of slope and intercept?

Tip: When analyzing a graph, always identify at least two clear points on the line to accurately determine the slope.