Chapter 4.2, Problem 51HP

To determine

Linear equations are useful in predicting future events. Describe some factors in real-world situations that might affect the reliability of the graph in making any predictions.

Explanation of Solution

Linear equations can be used to predict something that has a constant of rate of change.

Since , the slope that we see in the slope-intercept form , is always constant .

And any linear equation can be converted easily into slope-intercept form .

  $\begin{array}{l}ax+by=c\mathrm{...................................}[linear\_equation]\\ \Rightarrow by=c-ax\mathrm{...............................}[subtract"ax"each\_side]\\ \Rightarrow y=-\frac{a}{b}x+\frac{c}{b}\mathrm{...........................}[slope-\mathrm{int}ercept]\\ y=mx+c\mathrm{....................................}[slope-intercept]\\ m=slope=constant\\ c=y-intercept\end{array}$

Hence, if any event or situation does not have a constant rate of change like prices in stock market or sudden change in weather ,

The graph suddenly spikes up or down in such situations and if would be hard to predict anything prior to the real-event.

This also happens in gambling.