The rate of change is constant in each table. Find the rate of change. Explain what the rate of change means for the situation. time (hours) 4, 6, 8, 10 distance (miles) 212, 318, 424, 530

[tex]\bf \begin{array}{ccll} \stackrel{\stackrel{x}{hours}}{time}&\stackrel{\stackrel{y}{miles}}{distance}\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 4&212\\ \boxed{6}&\boxed{318}\\ 8&424\\ \boxed{10}&\boxed{530} \end{array}\\\\ -------------------------------[/tex]

[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 6}}\quad ,&{{ 318}})\quad % (c,d) &({{ 10}}\quad ,&{{ 530}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{530-318}{10-6}\implies \cfrac{212}{4} \\\\\\ \stackrel{\textit{average rate of change}}{\cfrac{53}{1}}[/tex]

recall the top is distance, and the bottom is hours, so 53 miles for every 1 hour.  So the object or vehicle is moving at 53 mph on average.