From the diagram below, find the positive difference in the x-coordinates when lines l and m reach y = 15.
+9466 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 = \(\frac{79}{2}\)
