Difference between revisions of "2018 AMC 12B Problems/Problem 3"
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| − | A line with slope 2 intersects a line with slope 6 at the point <math>(40,30)</math>. What is the distance between the x-intercepts of these two lines? | + | A line with slope 2 intersects a line with slope 6 at the point <math>(40,30)</math>. What is the distance between the <math>x</math>-intercepts of these two lines? |
<math>(\text{A}) 5 \qquad (\text{B}) 10 \qquad (\text{C}) 20 \qquad (\text{D}) 25 \qquad (\text{E}) 50</math> | <math>(\text{A}) 5 \qquad (\text{B}) 10 \qquad (\text{C}) 20 \qquad (\text{D}) 25 \qquad (\text{E}) 50</math> | ||
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| + | ===Solution 1=== | ||
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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 | ||
Revision as of 14:03, 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
