Answer:
The linear function is given by:
[tex]y=\dfrac{3}{2}x-\dfrac{7}{2}[/tex]
Step-by-step explanation:
It is given that the rate of change of the linear function is equal to the average rate of change of function f on the interval [-1, 1].
The slope(m) or average rate of change of the linear function will be:
[tex]m=\dfrac{f(1)-f(-1)}{1-(-1)}\\\\\\m=\dfrac{-2-(-5)}{1+1}\\\\\\m=\dfrac{-2+5}{2}\\\\\\m=\dfrac{3}{2}[/tex]
and the linear function pass through (1,-2)
We know that the equation of a line with given slope m and passing through point (a,b) is given by:
Here (a,b)=(1,-2)
and [tex]m=\dfrac{3}{2}[/tex]
Hence, the equation of linear function is:
[tex]y-(-2)=\dfrac{3}{2}\times (x-1)\\\\\\y+2=\dfrac{3}{2}x-\dfrac{3}{2}\\\\\\y=\dfrac{3}{2}x-\dfrac{3}{2}-2\\\\\\y=\dfrac{3}{2}x-\dfrac{7}{2}[/tex]
