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Identifying Intercepts from Graphs of Lines
To find the intercepts of a line from its graph, locate the points where the line crosses each coordinate axis. By inspecting the graphs of four different linear equations on a rectangular coordinate system, we can identify their intercepts:
- Figure (a): The line crosses the -axis at , giving an -intercept of . It crosses the -axis at , giving a -intercept of .
- Figure (b): The line crosses the -axis at (-intercept: ) and crosses the -axis at (-intercept: ).
- Figure (c): The line crosses the -axis at (-intercept: ) and crosses the -axis at (-intercept: ).
- Figure (d): The line passes directly through the origin, meaning it crosses both the -axis and -axis at . Thus, both the -intercept and -intercept are the same point: . In every general case, the point where the line crosses the -axis takes the ordered pair form , and where it crosses the -axis takes the form .
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