$y_A$ 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?

  • $\begingroup$ 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

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.

  • $\begingroup$ 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

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.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.