Q:

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

Accepted Solution

A:
Answer:see the explanationStep-by-step explanation:Part ASaraFind out the equation of the lineThe equation of the line in slope intercept  form is equal to[tex]y=mx+b[/tex]wherem is the slopeb is the y-interceptx is the number of monthsy is the number of comic bookswe have[tex]b=12\ comic\ books[/tex]Find the slope mwe have the points(0,12) and (4,20)[tex]m=(20-12)/(4-0)\\m=2\ comic/month[/tex]substitute[tex]y=2x+12[/tex]Each unit on the x-axis represent 0.5 months and each unit  on the y-axis represent 4 comic booksThe 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)AshtonFind out the equation of the lineThe equation of the line in slope intercept  form is equal to[tex]y=mx+b[/tex]wherem is the slopeb is the y-interceptx is the number of monthsy is the number of comic bookswe have[tex]b=2\ comic\ books[/tex][tex]m=3\ comic/month[/tex]substitute[tex]y=3x+2[/tex]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 BCompare the slope and y-intercept for the graphs of each function in terms of the quantitiesSara[tex]b=12\ comic\ books[/tex][tex]m=2\ comic/month[/tex]Ashton[tex]b=2\ comic\ books[/tex][tex]m=3\ comic/month[/tex]thereforeSara's graph has the greater y-intercept than Ashton's graphAshton's graph has the greater slope than Sara's graph