Question

The office manager ordered 140 reams of printer paper. Based on average daily use, they know that 140 reams of paper will last about 80 days. Write the equation in slope intercept form and graph this situation.
Define variables:
Let x = ?
Let y = ?

The equation in slope-intercept form is:

What is the reasonable domain for this situation?

What is the reasonable range for this situation?

What is the rate of change and what does it represent?

What does the x-intercept represent in this situation?

What does the y-intercept represent in this situation?

Answer 1

Let

x--------> the number of days

y--------> the number of reams of paper

we know that

For x=0 days  y=140 reams of paper--------> point A(0,140)

The point A is the y-intercept -----> remember that the y-intercept is the value of y when the value of x is equal to zero

For x=80 days  y=0 reams of paper--------> point B(80,0)

The point B is the x-intercept -----> remember that the x-intercept is the value of x when the value of y is equal to zero

Step 1  

Find the equation in slope-intercept form

Find the slope of the points A and B

m=(y2-y1)/(x2-x1)

substitute

m=(0-140)/(80-0)-------> m=-140/80

$m=-1.75 \frac{reams}{day}$

the equation in slope-intercept form is equal to

y=mx+b

b is the coordinate of y in the y-intercept point

so

b=140

substitute

$y=-1.75x+140$

therefore

the answer part 1) is

the equation in slope-intercept form is equal to $y=-1.75x+140$

Step 2

Find the reasonable domain for this situation

the domain are the values for x

$x\geq0\\x\leq 80\\0\leq x \leq80$

therefore

the domain is the interval-------> [0,80]

Step 3

Find the reasonable range for this situation

the range are the values for y

$y\geq0\\y\leq 140\\0\leq y \leq140$

therefore

the range is the interval-------> [0,140]

Step 4

What is the rate of change and what does it represent?

the rate of change is the slope of the equation of the line

in this problem

$m=-1.75\frac{reams}{day}$

the rate of change represents the amount of reams that are consumed per day, is negative because each day is becoming smaller

Step 5

What does the x-intercept represent in this situation?

For x=80 days  y=0 reams of paper--------> point B(80,0)

The point B is the x-intercept -----> remember that the x-intercept is the value of x when the value of y is equal to zero

The x-intercept represents the day 80, day in which the amount of reams is zero

Step 6

What does the y-intercept represent in this situation?

For x=0 days  y=140 reams of paper--------> point A(0,140)

The point A is the y-intercept -----> remember that the y-intercept is the value of y when the value of x is equal to zero

The y-intercept represents the day 0, day in which the amount of reams is 140