# Question ac356

Oct 15, 2017

Average rate of change $= 7$
$y = 7 x - 8$

#### Explanation:

For the function y = f(x) between x = a, and x = b, the

$f \left(x\right) = 2 {x}^{2} - 3 x$
$f \left(a\right) = 2 - 3 = - 1 , w h e n \textcolor{w h i t e}{a a} a = 1$

$f \left(b\right) = 32 - 12 = 20 , w h e n \textcolor{w h i t e}{a a} b = 4$

a=1, f(a)=-1; b=4, f(b)=20#

Average rate of change $= \frac{f \left(b\right) - f \left(a\right)}{b - a} = \frac{20 - \left(- 1\right)}{4 - 1}$
$= \frac{21}{3} = 7$

$y = m x + c$; to find c,
$- 1 = \left(7 \cdot 1\right) + c$
$c = - 8$

The function is
$y = 7 x - 8$