We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
309
1
avatar

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

 Apr 8, 2018
 #1
avatar+7545 
+2

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  =  \(\frac{79}{2}\)

.
 Apr 8, 2018

29 Online Users

avatar
avatar
avatar