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

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

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Apr 8, 2018