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 = \(\frac{79}{2}\)
.Thelma invested $50,000 in 3 different investments at 6%, 7%, 9%. She invested $20,000 more in 9% than in 6%. If at the end of one year she received interest of $3,970 on her investments, how much did she invest in each of her 3 investments? Thank you for help.
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