Writing equations and calculating cost based on a graph

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The discussion focuses on modeling the cost of personalized dog accessories based on the number of letters in a dog's name. The equation y = mx + b is used, where y is the total cost, m represents the slope (cost per additional letter), x is the number of additional letters, and b is the base fee. The initial interpretation of the slope and intercept was incorrect, leading to confusion about the cost structure, but through collaboration, the correct slope of 1.25 and base fee of $11 were established. Participants emphasized the importance of accurately reading the graph to determine the relationship between additional letters and cost. Ultimately, the correct equation for the cost is y = 1.25x + 11, reflecting the accurate pricing model for the service.
  • #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.
 
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  • #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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