Writing equations and calculating cost based on a graph

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SUMMARY

The discussion centers on modeling the cost of personalized dog accessories from the Doggone Leash Company using the equation y = mx + b. The basic fee for the first 10 letters is $11, with an additional charge of $1 for each letter beyond that. Participants clarify the correct interpretation of the slope (m) and y-intercept (b) in the context of the cost equation. The final equation derived is y = 1.25x + 11, where x represents the number of additional letters.

PREREQUISITES
  • Understanding of linear equations, specifically the slope-intercept form (y = mx + b).
  • Basic knowledge of graph interpretation and how to derive points from a graph.
  • Ability to perform arithmetic operations to calculate slope and intercept.
  • Familiarity with the concept of cost modeling in a business context.
NEXT STEPS
  • Learn how to derive equations from graphs using two-point slope calculations.
  • Study the implications of slope and intercept in real-world applications.
  • Explore cost modeling techniques for service-based businesses.
  • Investigate how to create and interpret tables of values for linear equations.
USEFUL FOR

Students studying algebra, particularly those focusing on linear equations and their applications in real-world scenarios, as well as business analysts interested in cost modeling.

  • #31
So if it is 11, would that mean that y = 1.25x + 11?
 
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  • #32
Kirito123 said:
So if it is 11, would that mean that y = 1.25x + 11?

You can verify whether you are correct by choosing a random point and fill the x and y in in the equation. When you get something like '3 = 3', you are correct. Do you get something like '3=4', you made a mistake. Every single point of the line is given by this equation (if correct) .
 
  • #33
No I am wrong then cause if i plug in x and y as 2 for example i would get like 2 = 15 (near 15).
 
  • #34
SammyS said:
And the question Math_IQ asks is: "What do you get for b ?"

(I think you already have it.)
Kirito123 said:
No I am wrong then cause if i plug in x and y as 2 for example i would get like 2 = 15 (near 15).
2×1.25 = 2.50

2.50 +11.00 = 13.50

Looks good to me !
 
  • #35
O i thought i was wrong cause if i put 3 = 1.25(3) + 11 it doesn't make 3 =3 or did i not understand what math_qed mean't.
 
Last edited:
  • #36
So if I am correct should i just use that formula to solve for the graph i made?
 
  • #37
Kirito123 said:
So if I am correct should i just use that formula to solve for the graph i made?
Yes, make a chart for prices all the way from 0 extra letters all the way to 12 extra letters. When finished, make sure it agrees with the graph.
 
  • #38
ok
 
  • #39
Yes that formula is right. i tried it with 0 , 1 , 2, and 3 and i got the same answer as shown on the graph. I think the whole reason i got it wrong was because i didn't look a the graph closely. i think i can do the rest now. Thx a lot :)
 
  • #40
Try larger values of x.

Check a larger range of the graph.

x=6, 8, 9,12 .
 
  • #41
ok i will
 
  • #42
Ok i tested it out for 6 and other numbers and i got the right answer, (srry for the late reply). But anyway that proves the formula is right and THX SO MUCH.

if I am wrong pls correct me. Formula : y = 1.25x + 11
 
  • #43
Kirito123 said:
Ok i tested it out for 6 and other numbers and i got the right answer, (srry for the late reply). But anyway that proves the formula is right and THX SO MUCH.

if I am wrong pls correct me. Formula : y = 1.25x + 11

Seems good.
 
  • #44
thank you again.
 
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