2003 AMC 10B Problems/Problem 11
Problem
A line with slope intersects a line with slope at point . What is the distance between the -intercepts of these two lines?
Solution 1
Using the point-slope form, the equation of each line is
Substitute in to find the -intercepts.
The difference between them is .
Solution 2(using slopes)
The -intercepts of a line is where the line's -coordinate is . The slope is defined as . Therefore, the line with slope can be expressed as
From to the -intercept, the line must move units to the -axis. Therefore, .
Therefore, the -intercept of the line with slope is .Note that some sources may state "the -intercept is " instead of "the -intercept is .
If an idea functions great for one part of the problem but does not find the solution to the problem, we want to use the idea again. Using the idea for the line with slope , we find . Therefore, the -intercept of the line with slope is . The distance between .
See Also
2003 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
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All AMC 10 Problems and Solutions |
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