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
[tex]m=-1.75 \frac{reams}{day}[/tex]
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
[tex]y=-1.75x+140[/tex]
therefore
the answer part 1) is
the equation in slope-intercept form is equal to [tex]y=-1.75x+140[/tex]
Step 2
Find the reasonable domain for this situation
the domain are the values for x
[tex]x\geq0\\x\leq 80\\0\leq x \leq80[/tex]
therefore
the domain is the interval-------> [0,80]
Step 3
Find the reasonable range for this situation
the range are the values for y
[tex]y\geq0\\y\leq 140\\0\leq y \leq140[/tex]
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
[tex]m=-1.75\frac{reams}{day}[/tex]
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
