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$y_A$ and $y_B$ represent continuous linear relations. Some values from the relations are shown in the table below.

\begin{array}{|c|c|c|} \hline x & y_A & y_B \\ \hline -8 & -5 & -15 \\ \hline -3 & -6 & -11 \\ \hline \end{array}

How do I solve this system? Do I find the slope and then solve for the y intercept to find both equations, and then graph them to find where they intersect?

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  • $\begingroup$ Try looking at cause and effect. Just a quick glance at the table shows that an increase of $5$ in $x$ results in a decrease of $1$ in $y_A$ and an increase of $4$ in $y_B$. Logic would dictate that if we keep increasing $x$ that $y_A$ and $y_B$ will eventually meet in the middle. $\endgroup$ – John Joy Aug 19 '15 at 12:47
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Since the functions are linear, and you have 2 data points for each line, you could simply plot those two points and draw a line through them. Do that for both lines and see where they intersect. No calculations required.

To calculate the precise intercept you would typically calculate the gradients and $y$-intercept ($m$ and $c$). But I'm not sure your question is calling for this.

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  • $\begingroup$ So I plot (-8, -5) and (-3,-6) on the graph, but don't i need to find the slope for each? $\endgroup$ – Madison Aug 18 '15 at 18:59
  • $\begingroup$ Yes. And draw a line between them. Then plot (-8,-15) and (-3,-11) and draw a line between them too. The two lines will (hopefully) intercept and you can read off the interception point. You may have to extend the lines beyond the points. $\endgroup$ – Dr Xorile Aug 18 '15 at 19:03
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To solve by graphing, you plot both $y_A$ and $y_B$ as functions of $x$ (you will indeed need slope and intercept for that) and then find the intersection point.

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