Question

The total number of hats h(w) Ms. Sutton knitted is a function of the number of weeks w since she decided to sell them at a craft fair, as shown in the table. The function is a linear function.

What does the slope of the function represent?

This table is of a function.

Ms. Sutton knits 2 hats per week.

Ms. Sutton knits 4 hats per week.

Ms. Sutton knits a hat every 2 weeks.

Ms. Sutton knits a hat every 4 weeks.

Answer 1

The answer of a linear function is y=x^2

Answer 2

$\bf \begin{array}{l|lllllll} w&2&4&6&8&10\\\\ h(w)&\stackrel{2\cdot 2}{4}&\stackrel{2\cdot 4}{8}&\stackrel{2\cdot 6}{12}&\stackrel{2\cdot 8}{16}&\stackrel{2\cdot 10}{20} \end{array} \\\\\\ slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ h(w_2)}}-{{ h(w_1)}}}{{{ w_2}}-{{ w_1}}}\impliedby \begin{array}{llll} average\ rate\\ of\ change \end{array} \\\\\\ \cfrac{\textit{how many hats Ms Sutton makes}}{\textit{for every passing week}}$

notice, every h(w) value, is just twice as much as a w value.

so for every "w", she makes "2*w" hats.