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From the diagram below, find the positive difference in the x-coordinates when lines l and m reach y = 15. 

Guest Apr 8, 2018
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Line  \(l\)  appears to have a slope of  \(-\frac53\)  and a y-intercept of  5 .

 

So the equation of line  \(l\)  is           \(y\,=\,-\frac53x+5\)

 

On line  \(l\) ,  when  y  =  15 .....

 

\(15\,=\,-\frac53x+5\\~\\ 10\,=\,-\frac53x\\~\\ -\frac35\cdot10\,=\,x\\~\\ -6\,=\,x\)

 

So line  \(l\)  passes through the point  (-6, 15) .

 

Line  \(m\)  appears to have a slope of  \(-\frac27\)  and a y-intercept of  2 .

 

So the equation of line  \(m\)  is        \(y\,=\,-\frac27x+2\)

 

On line  \(m\) ,  when  y = 15 ....

 

\(15\,=\,-\frac27x+2\\~\\ 13\,=\,-\frac27x\\~\\ -\frac72\cdot13\,=\,x\\~\\ -\frac{91}{2}\,=\,x\)

 

So line  \(m\)  passes through the point  (\(-\frac{91}{2}\), 15)  .

 

Here's a graph to check this:   https://www.desmos.com/calculator/jbuxnl82ve

 

the difference in the x-coordinates  =  \(-6--\frac{91}{2}\,=\,-6+\frac{91}{2}\,=\,-\frac{12}{2}+\frac{91}{2}\,=\,\frac{79}{2}\)

 

the difference in the x-coordinates  =  \(\frac{79}{2}\)

hectictar  Apr 8, 2018

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