Horizontal and Vertical Intercepts from Graphs Determine the horizontal and vertical intercepts for each graph below Intercepts must be written aS ordered pairs: If an intercept does not exist, write DNE. Vertical Intercept: Horizontal Intercept: Vertical Intercept: Horizontal Intercept: 5+y 5 Vertical Intercept: Horizontal Intercept: Vertical Intercept: Horizontal Intercept:
The Correct Answer and Explanation is:
Here are the correct answers for the worksheet.
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Explanation of Horizontal and Vertical Intercepts
In coordinate geometry, the intercepts of a graph are the points where the graph crosses the coordinate axes. These points are crucial for understanding the position and orientation of a line or curve.
Vertical Intercept
The vertical intercept, often called the y-intercept, is the point where the graph intersects the vertical axis (the y-axis). A key feature of any point on the y-axis is that its x-coordinate is always 0. Therefore, the vertical intercept will always be in the form of an ordered pair (0, y).
Horizontal Intercept
The horizontal intercept, commonly known as the x-intercept, is the point where the graph intersects the horizontal axis (the x-axis). Similarly, any point on the x-axis has a y-coordinate of 0. Thus, the horizontal intercept will always be written as an ordered pair (x, 0).
Analysis of the Graphs:
- Top-Left Graph:
- Vertical Intercept: The line crosses the y-axis at the point where y is 1. Since the x-coordinate must be 0, the vertical intercept is (0, 1).
- Horizontal Intercept: The line crosses the x-axis at the point where x is 1. Since the y-coordinate must be 0, the horizontal intercept is (1, 0).
- Top-Right Graph:
- Vertical Intercept: The line intersects the y-axis at y = 2. This corresponds to the ordered pair (0, 2).
- Horizontal Intercept: The line intersects the x-axis at x = -4. This corresponds to the ordered pair (-4, 0).
- Bottom-Left Graph (Horizontal Line):
- Vertical Intercept: This horizontal line is defined by the equation y = -5. It crosses the y-axis at -5. The intercept is (0, -5).
- Horizontal Intercept: Because the line is horizontal and not the x-axis itself, it is parallel to the x-axis and will never cross it. Therefore, a horizontal intercept Does Not Exist (DNE).
- Bottom-Right Graph (Vertical Line):
- Vertical Intercept: This vertical line is defined by the equation x = -4. As it is parallel to the y-axis, it will never intersect it. Thus, a vertical intercept Does Not Exist (DNE).
- Horizontal Intercept: The line crosses the x-axis at x = -4. The intercept is (-4,
