Chapter 3, Problem 4RE

(a)

To determine

To find: The slope and y-intercept of linear function $F\left(x\right)=-\frac{1}{3}x+1$ .

Answer to Problem 4RE

Slope $=-\frac{1}{3}$

y-intercept $=1$

Explanation of Solution

Given: $F\left(x\right)=-\frac{1}{3}x+1$

Slope: The coefficient of x of linear function.

Slope $=-\frac{1}{3}$

y-intercept: The constant part of the function.

y-intercept $=1$

(b)

To determine

To find:Theaverage rate of change of function $F\left(x\right)=-\frac{1}{3}x+1$ .

Answer to Problem 4RE

  $-\frac{1}{3}$

Explanation of Solution

Given: $F\left(x\right)=-\frac{1}{3}x+1$

The average rate of change of linear function is constant. Average rate is change in y over change in x.

In another way, It would be slope of linear function.

Therefore, the average rate is $-\frac{1}{3}$ .

(c)

To determine

To graph: Thelinear function $F\left(x\right)=-\frac{1}{3}x+1$ .

Answer to Problem 4RE

  

Explanation of Solution

Given: $F\left(x\right)=-\frac{1}{3}x+1$

The given linear function, $F\left(x\right)=-\frac{1}{3}x+1$ .

First make the table of x and y. By taking some random value of x

  $\begin{array}{cccc}x& -3& 0& 3\\ y& 2& 1& 0\end{array}$

Now plot the points on graph.

  

(d)

To determine

To find: The increasing, decreasing or constant of function $F\left(x\right)=-\frac{1}{3}x+1$ .

Answer to Problem 4RE

decreasing

Explanation of Solution

Given: $F\left(x\right)=-\frac{1}{3}x+1$

The average rate of change of linear function is constant. Average rate is change in y over change in x.

In another way, It would be slope of linear function.

The rate of the function is negative. If the rate of linear function is negative then it would be decreasing function.