Difference between revisions of "2018 AMC 12B Problems/Problem 3"
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| − | Using the slope-intercept form, we get the equations <math>y-30 = 6(x-40)</math> and <math>y-30 = 2(x-40)</math>. Simplifying, we get <math>6x-y=210</math> and <math>2x-y=50</math>. Letting <math>y=0</math> in both equations gives the <math>x</math>-intercepts | + | Using the slope-intercept form, we get the equations <math>y-30 = 6(x-40)</math> and <math>y-30 = 2(x-40)</math>. Simplifying, we get <math>6x-y=210</math> and <math>2x-y=50</math>. Letting <math>y=0</math> in both equations gives the <math>x</math>-intercepts: <math>x=35</math> and <math>x=25</math>, respectively. Thus the distance between them is <math>35-25 = 10 \rightarrow (\text{B})</math> |
Revision as of 15:05, 16 February 2018
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?
Solution 1
Using the slope-intercept form, we get the equations 
and 
. Simplifying, we get 
and 
. Letting 
in both equations gives the -intercepts: 
and 
, respectively. Thus the distance between them is 
