\begin{frame} \frametitle{Motivation and Overview} \scalebox{.8}{ \begin{tikzpicture}[default] \def\diax{\text{time}} \def\diay{\text{speed}} \def\diaborderx{.75cm} \def\diabordery{.75cm} \diagram[1]{-1}{4}{-1}{8}{1} \diagramannotatez \diagramannotatexx{1/1h,2/2h,3/3h} \diagramannotateyy{1/10 \text{mph},2/20 \text{mph},3/30 \text{mph},3/30 \text{mph}} \draw[cred] plot[smooth,domain=0:1,samples=20] (\x,{1}); \draw[cred] plot[smooth,domain=1:2,samples=20] (\x,{2}); \draw[cred] plot[smooth,domain=2:3,samples=20] (\x,{3}); \onslide<2->{ \draw[draw=none,fill=cred,opacity=.5] plot[ybar interval,domain=0:1,samples=2] (\x,{1}); } \onslide<3->{ \draw[draw=none,fill=cred,opacity=.5] plot[ybar interval,domain=1:2,samples=2] (\x,{2}); } \onslide<4>{ \draw[draw=none,fill=cred,opacity=.5] plot[ybar interval,domain=2:3,samples=2] (\x,{3}); } \onslide<5->{ \draw[draw=none,fill=cred,opacity=.5] plot[ybar interval,domain=2:2.5,samples=2] (\x,{3}); \draw[dashed,cblue] (2.5,-.5) -- node [at end,above] {time $2.5h$} (2.5,6.5); \node at (1.25,.5) {area = $45$}; } \begin{scope}[xshift=.65\textwidth] \def\diax{\text{time}} \def\diay{\text{distance}} \def\diaborderx{.75cm} \def\diabordery{.75cm} \diagram[1]{-1}{4}{-1}{8}{1} \diagramannotatez \diagramannotatexx{1/1h,2/2h,3/3h} \diagramannotateyy{1/10 \text{mi},2/20 \text{mi},3/30 \text{mi},4/40 \text{mi},5/50 \text{mi},6/60 \text{mi},7/70 \text{mi}} \pause \node[cred,include] at (1,1) {}; \draw[cred] plot[smooth,domain=0:1,samples=20] (\x,{\x}); \pause \node[cred,include] at (2,3) {}; \draw[cred] plot[smooth,domain=1:2,samples=20] (\x,{2*\x-1}); \pause \node[cred,include] at (3,6) {}; \draw[cred] plot[smooth,domain=2:3,samples=20] (\x,{3*\x-3}); \pause \node[include,cblue] at (2.5,4.5) {}; \draw[dashed,cblue] (2.5,-.5) -- node [at end,above] {time $2.5h$} (2.5,6.5); \end{scope} \begin{scope}[line width=2mm,cgreen,->] \onslide<6->{ \draw[opacity=.7] (1.5,1) to[bend left=23] (9,4.3); \path[decoration={text along path,raise=2mm,text={area is distance\ \ \ \ \ \ },text align={center}},decorate] (1.5,1) to[bend left=23] (9,4.3); } \onslide<7->{ \draw[opacity=.7] (9,4.9) to[bend left=-25] (2.9,3.4); \path[decoration={text along path,raise=2mm,text={slope is speed\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ },text align={center}},decorate] (2.9,3.4) to[bend left=25] (9,4.9); } \end{scope} \pause \pause \end{tikzpicture} } \end{frame}