Question

creating a cost equation
you buy a printer for $80 and then pay $15 for each ink cartridge that you use.
the statement can be represented by the equation $y = 15x + 80$.

a. complete the table to represent the total cost for 0 to 4 cartridges.

number of cartridges, $x$	cost, $y$ (dollars)
1
2
3
4

domain: {0,1,2,3,4}
range:
{ __ , , , , __ }

b. graph the points from part a

graph with x-axis: number of cartridges (0 to 4) and y-axis: cost (c) dollars (0 to 160)

c. using the table, check that $x$ has a constant change between consecutive terms.

$1 - 0 = $ ____
$2 - 1 = $ ____
$3 - 2 = $ ____
$4 - 3 = $ ____

d. now check that $y$ has a constant change between consecutive terms. the first one is done for you.

$\underline{95} - \underline{80} = \underline{15}$
__ - = __
__ - = __
__ - = __

e. a change in $x$ of __ corresponds to a change in $y$ of __. this equation is linear.

note: linear equations grow by equal differences over equal intervals.

Explanation:

Part A

Step1: Calculate for x=1

Substitute \( x = 1 \) into \( y = 15x + 80 \).
\( y = 15(1) + 80 = 15 + 80 = 95 \)

Step2: Calculate for x=2

Substitute \( x = 2 \) into \( y = 15x + 80 \).
\( y = 15(2) + 80 = 30 + 80 = 110 \)

Step3: Calculate for x=3

Substitute \( x = 3 \) into \( y = 15x + 80 \).
\( y = 15(3) + 80 = 45 + 80 = 125 \)

Step4: Calculate for x=4

Substitute \( x = 4 \) into \( y = 15x + 80 \).
\( y = 15(4) + 80 = 60 + 80 = 140 \)

Step5: Determine the range

The range is the set of y - values for \( x = 0,1,2,3,4 \), which are 80, 95, 110, 125, 140.

Step1: Calculate \( 1 - 0 \)

\( 1-0 = 1 \)

Step2: Calculate \( 2 - 1 \)

\( 2 - 1=1 \)

Step3: Calculate \( 3 - 2 \)

\( 3 - 2 = 1 \)

Step4: Calculate \( 4 - 3 \)

\( 4 - 3=1 \)

Step1: Calculate the difference for the second pair

We know the y - values are 80, 95, 110, 125, 140. For the second pair, we take 110 and 95.
\( 110-95 = 15 \)

Step2: Calculate the difference for the third pair

Take 125 and 110.
\( 125 - 110=15 \)

Step3: Calculate the difference for the fourth pair

Take 140 and 125.
\( 140 - 125 = 15 \)

Answer:

(Part A Table):

Number of cartridges, \( x \)	Cost, \( y \) (dollars)
1	95
2	110
3	125
4	140