Chapter 3, Problem 9STP

To determine

The equation in function notation

Answer to Problem 9STP

The equation in function notation is $n=0.45h$ .

Option B is correct

Explanation of Solution

Given information:

  

The pair of points in table $\left(1,0.45\right),\left(2,0.9\right)\text{,}\left(3,1.35\right)\text{and }\left(4,1.8\right)$

Concept Used:

The slope of a line connecting the points $\left(h_1,n_1\right),\text{ and }\left(h_2,n_2\right)$ is given by the formula

  $\text{Slope }\left(m\right)=\frac{n_2-n_1}{h_2-h_1}$

The equation for line is $n-n_1=m\left(h-h_1\right)$

Calculation:

In order to find the average rate of change the points

  $\left(1,0.45\right),\text{ and }\left(2,0.9\right)$ , use the slope formula and substitute the values $\left(h_1,n_1\right)=\left(1,0.45\right),\text{ and }\left(h_2,n_2\right)=\left(2,0.9\right)$ and simplify further as shown below,

  $\begin{array}{c}\text{Slope }\left(m\right)=\frac{n_2-n_1}{h_2-h_1}\\ =\frac{0.9-0.45}{2-1}\\ =0.45\\ \text{Equation}\text{in}\text{function}\text{notation }\text{is}\\ n-n_1=m\left(h-h_1\right)\\ n-0.45=0.45\left(h-1\right)\\ n-0.45=0.45h-0.45\\ n-0.45+0.45=0.45h-0.45+0.45\\ n=0.45h\end{array}$

Thus, the equation in function notation is $n=0.45h$ .

Option B is correct