Question

What is the rate of change for y = -3x + 2 over the interval [-3, 4]?

Answer 1

$\bf slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ f(x_2)}}-{{ f(x_1)}}}{{{ x_2}}-{{ x_1}}}\impliedby \begin{array}{llll} average\ rate\\ of\ change \end{array}\\\\ -------------------------------\\\\ \stackrel{y}{f(x)}= -3x+2 \qquad \begin{cases} x_1=-3\\ x_2=4 \end{cases}\implies \cfrac{f(4)-f(-3)}{4-(-3)} \\\\\\ \cfrac{[-3(4)+2]~~-~~[-3(-3)+2]}{4+3}\implies \cfrac{-10~~-~~[11]}{7} \\\\\\ \cfrac{-21}{7}\implies \cfrac{-3}{1}\implies -3$