For the two graphs in the image, we are asked to determine the x- and y-intercepts of each line.

Problem 24:

• The line is diagonal and sloping upward from left to right.
• To find the x-intercept: Look at where the line crosses the x-axis (where $y = 0$). The line crosses the x-axis at $x = 2$. Therefore, the x-intercept is $(2, 0)$.
• To find the y-intercept: Look at where the line crosses the y-axis (where $x = 0$). The line crosses the y-axis at $y = -2$. Therefore, the y-intercept is $(0, -2)$.

Problem 25:

• The line is horizontal, meaning it is constant at $y = 2$.
• For a horizontal line, there is no x-intercept because the line never crosses the x-axis.
• The y-intercept is where the line crosses the y-axis. In this case, the line crosses the y-axis at $y = 2$. Therefore, the y-intercept is $(0, 2)$.

Would you like further details or explanations?

Additional questions:

1. How do you find the intercepts of a line algebraically from its equation?
2. What is the significance of a horizontal line in terms of slope?
3. How would a vertical line look on this type of graph, and what are its intercepts?
4. Can a line have multiple x- or y-intercepts? Why or why not?
5. What is the slope of the line in problem 24 based on the graph?

Tip:

To find intercepts easily, remember: set $y = 0$ to find the x-intercept and set $x = 0$ to find the y-intercept.