Difference between revisions of "2003 AMC 10B Problems/Problem 11"
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Substitute in <math>y=0</math> to find the <math>x</math>-intercepts. | Substitute in <math>y=0</math> to find the <math>x</math>-intercepts. | ||
| − | <cmath>0=3x-15\ | + | <cmath>0=3x-15\longrightarrow x=5\\ |
| − | 0=5x-35\ | + | 0=5x-35\longrightarrow x=7</cmath> |
The difference between them is <math>7-5=\boxed{\textbf{(A) \ } 2}</math>. | The difference between them is <math>7-5=\boxed{\textbf{(A) \ } 2}</math>. | ||
Revision as of 18:05, 31 December 2013
Problem
A line with slope 
intersects a line with slope 
at point 
. What is the distance between the 
-intercepts of these two lines?
Solution
Using the point-slope formula, the equation of each line is
![\[y-15=3(x-10) \longrightarrow y=3x-15\\ y-15=5(x-10) \longrightarrow y=5x-35\]](http://latex.artofproblemsolving.com/1/3/9/139440d80ffaa565a0d8b96c27d98b374b8d3f04.png)
Substitute in 
to find the -intercepts.
![\[0=3x-15\longrightarrow x=5\\ 0=5x-35\longrightarrow x=7\]](http://latex.artofproblemsolving.com/e/d/4/ed4f6885af7da3b46b4d2ee19040a25e1e68d719.png)
The difference between them is 
.
See Also
| 2003 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 10 |
Followed by Problem 12 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
