Question

This question has 2 parts. Answer both parts. Sara started with 12 comic books in her collection. She collected the same number of comic books each month until she had 20 comic books in the 4th month. Ashton started with 2 comic books in his collection and continues to collect 3 comic books each month.

Part A

Interpret the origin on the graph. Also, describe the scale of each axis by telling what does each unit on the x-axis and the y-axis represent.


Part B

Compare the slope and y-intercept for the graphs of each function in terms of the quantities.

Answer 1

see the explanation

Explanation:

Part A

Sara

Find out the equation of the line

The equation of the line in slope intercept form is equal to

`y=mx+b`

where

m is the slope

b is the y-intercept

x is the number of months

y is the number of comic books

we have

`b=12\ comic\ books`

Find the slope m

we have the points

(0,12) and (4,20)

`m=(20-12)/(4-0)\\m=2\ comic/month`

substitute

`y=2x+12`

Each unit on the x-axis represent 0.5 months and each unit on the y-axis represent 4 comic books

The origin of the graph is the point (0,12), this point represent the y-intercept or the initial value (the value of y when the value of x is equal to zero)

Ashton

Find out the equation of the line

The equation of the line in slope intercept form is equal to

`y=mx+b`

where

m is the slope

b is the y-intercept

x is the number of months

y is the number of comic books

we have

`b=2\ comic\ books`

`m=3\ comic/month`

substitute

`y=3x+2`

The origin of the graph is the point (0,2), this point represent the y-intercept or the initial value (the value of y when the value of x is equal to zero)

Part B

Compare the slope and y-intercept for the graphs of each function in terms of the quantities

Sara

`b=12\ comic\ books`

`m=2\ comic/month`

Ashton

`b=2\ comic\ books`

`m=3\ comic/month`

therefore

Sara's graph has the greater y-intercept than Ashton's graph

Ashton's graph has the greater slope than Sara's graph