[tex]\textbf{Answer:}[/tex]
[tex]\frac{-1}{4}[/tex]
[tex]\textbf{Step-by-step explanation:}[/tex]
[tex]\frac{y2 - y1}{x2 - x1}[/tex]
[tex]\textrm{Use the formula above to determine the rate of change}[/tex]
[tex]\frac{1 - 2}{4 - 0} \rightarrow\frac{-1}{4}[/tex]
[tex]\textrm{The rate of change of this line is }[/tex] [tex]\frac{-1}{4}[/tex]
recall that all we need is two points off a straight line to get its slope, so... hmmm this one passes through (0 , 2) and (4 , 1), so let's use those
[tex]\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-2}{4-0}\implies -\cfrac{1}{4}[/tex]
