Chapter 3, Problem 3RE

(a)

To determine

To find: the slope and y-intercept of the given linear function.

Answer to Problem 3RE

Slope $m=\frac{4}{5}$ and $y$ intercept, $b=-6$

Explanation of Solution

Given:

  $h(x)=\frac{4}{5}x-6$

Calculation:

The slope intercept form of a line is $y=mx+c$

Where the slope of the line is $m$ ,

And $y$ intercept is $b$ .

Compare the function $h(x)=\frac{4}{5}x-6$ with slope intercept form.

Slope $m=\frac{4}{5}$ and $y$ intercept, $b=-6$

Conclusion:

Therefore, the slope $m=\frac{4}{5}$ and $y$ intercept, $b=-6$

(b)

To determine

To find: the average rate of change of the given function

Answer to Problem 3RE

The rate of change $=\frac{4}{5}$

Explanation of Solution

Given:

The linear function $h(x)=\frac{4}{5}x-6$

For calculating average rate of change to given function, it is needed two points $Y$ intercept (0,-6) is one point and for second point

Let $x=5$

  $f(5)=\frac{4}{5}\times 5-6$

  $=\frac{20}{5}-6$

  $=4-6$

  $=-2$

So second point in $(x,y)$ form is (5,-2)

Now as rate of change $\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$

Here $x_1=0,y_1=-6,x_2=5,y_2=-2$

So rate of change $=\frac{-2-(-6)}{5-0}$

  $=\frac{-2+6}{5}$

  $=\frac{4}{5}$

Conclusion:

Therefore, the rate of change $=\frac{4}{5}$

(c)

To determine

To graph: the given function.

Answer to Problem 3RE

  

Explanation of Solution

Calculation:

The line joining two points (0,-6) and (5,-2) is shown as below where (7.5,0) is x intercept.

  

Conclusion:

Thus, the given function is drawn.

(d)

To determine

whether the function is increasing decreasing or constant.

Answer to Problem 3RE

Thus function is increasing in the interval $[-\infty ,+\infty ]$

Explanation of Solution

Calculation:

As the slope of the function $h(x)=\frac{4}{5}x-6$ is $\frac{4}{5},$ which is positive.

That means it is increasing function.

Thus function is increasing in the interval $[-\infty ,+\infty ]$

Conclusion:

Thus function is increasing in the interval $[-\infty ,+\infty ]$