Chapter 3, Problem 1RE

(a)

To determine

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

Answer to Problem 1RE

Slope $m=2$ and $y$ intercept $b=-5$

Explanation of Solution

Given:

  $f(x)=2x-5$

Calculation:

Theslope intercept form of a line as $y=mx+b$

Where the slope of the line is $m$

And $y$ intercept is $b$ .

Compare function $f(x)=2x-5$ with slope intercept form

Slope $m=2$ and $y$ intercept $b=-5$

Conclusion:

Therefore, the slope $m=2$ and $y$ intercept $b=-5$

(b)

To determine

To find:the average rate of change of each function

Answer to Problem 1RE

The rate of change is 2

Explanation of Solution

Given:

  $f(x)=2x-5$

Calculation:

For calculating average rate of change of given function. Any two points for it are needed. Y intercept is our one point. That is (0,-5) and

For second point

Let $x=1$

  $f(1)=2\times 1-5$

  $=2-5$

  $=-3$

So second point in $(x,y)$ form is (1,-3)

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

Here $x_1=0,y_1=-5,x_2=1,y_2=-3$

So rate of change $=\frac{-3-(-5)}{1-0}$

  $=\frac{-3+5}{1}$

  $=\frac{2}{1}$

  $=2$

Conclusion:

The rate of change is 2

(c)

To determine

To graph: the given function.

Explanation of Solution

Calculation:

The line joining two points (0,-5) and (1,-3) is shown as below

  

Conclusion:

Thus, the given function is drawn.

(d)

To determine

whether the function is increasing decreasing or constant.

Answer to Problem 1RE

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

Explanation of Solution

Calculation:

As the slope of the given function is 2 that is positive, that means its increasing function as if

slope is positive that means this line makes a positive acute angle with positive side of $x$ axis. Thus function is increasing in the interval $[-\infty ,+\infty ]$

Conclusion:

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