Math Problem Statement
Solution
From the uploaded image, I can assist you in determining the vertical and horizontal intercepts of the two graphs shown. Here's how to calculate them:
Left Graph:
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The line is horizontal, so it intersects the y-axis at one point.
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Vertical intercept (y-intercept):
The line crosses the y-axis at . -
Horizontal intercept (x-intercept):
Since the line is horizontal and does not cross the x-axis, there is no horizontal intercept.
Answer for the Left Graph:
- Vertical Intercept:
- Horizontal Intercept: None
Right Graph:
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The line is diagonal, so it intersects both axes.
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Vertical intercept (y-intercept):
The line crosses the y-axis at .
This point is . -
Horizontal intercept (x-intercept):
The line crosses the x-axis at .
This point is .
Answer for the Right Graph:
- Vertical Intercept:
- Horizontal Intercept:
Would you like further clarification or help plotting similar intercepts?
Here are 5 related questions to expand on the concept:
- How can you calculate the slope of a diagonal line like the one in the right graph?
- What are the general forms of equations for horizontal and diagonal lines?
- How do changes in slope affect the intercepts of a line?
- Can a line have multiple intercepts on the same axis? Why or why not?
- How do vertical lines differ in intercept characteristics compared to horizontal ones?
Tip: Always remember that the y-intercept occurs where and the x-intercept occurs where .
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Math Problem Analysis
Mathematical Concepts
Coordinate Geometry
Intercepts
Linear Equations
Formulas
Vertical intercept occurs where x = 0
Horizontal intercept occurs where y = 0
Theorems
Intercept Theorem: Intercepts of a line represent its intersection points with the axes.
Suitable Grade Level
Grades 8-10