Problem:
A line with slope 2 intersects a line with slope 6 at the point . What is the distance between the -intercepts of these two lines?
Answer Choices:
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Solution:
The line with slope 2 containing the point has the equation . Similarly, the line with slope 6 containing the point has the equation . To find the -intercepts of these two lines, let and solve for separately in each of these two equations. With the first equation the -intercept is 25 , and with the second equation the -intercept is 35 . Thus the distance between the two -intercepts is .
OR
As the line with slope 2 rises from to increases by 15 . As the line with slope 6 rises from to increases by 5 . Thus the distance between the -intercepts is .
The problems on this page are the property of the MAA's American Mathematics Competitions