C =number of pieces cut
Since the first cut is free, if C = 1, then TC = $2.25
TC = total cost
TC = 2.25 + (0.25)(C-1)
For 4 cuts,
TC = 2.25 + (0.25)(4-1)
TC = 2.25 + (0.25)(3)
TC = 2.25 + 0.75, TC = $3.00
Line is y = mx + b where m = slope, b is the constant.
In this case:
y = (0.25)(C-1) + 2.25, This will be a line. 0.25 is the slope, 2.25 is the constant, you can replace "x" for (C-1) as long as you understand that for each X > 2, x will equal (x-1) instead of "x"
y = 0.25x + 2.25
Here are some points to get you started. This line will not be a continuous one because x=0 has NO VALUE. In fact all real numbers between x = 0 and x = 1 have NO VALUE. This line will be a line that BEGINS at x=1 and will go off into infinity HOWEVER, THE LINE WILL NOT BE SOLID (you can not have 1/2 or 1/4 of a cut, so the "line" will be dotted instead of solid when you connect the dots. Understand?
Just know that the slope for this "line" is 0.25, (with each piece cut, cost is raised $0.25). Normal lines will not be like this. NORMAL LINES HAVE A CONSTANT SLOPE AND THE LINE WILL GO TO INFINITY IN EACH DIRECTION
THIS EQUATION REPRESENTS, IN GEOMETRY, SIMILAR TO A "RAY" with a starting point and then going into infinity into one direction, except in this case, instead of a solid line between points, there is a dotted line instead. Let me know if you have any other questions.
Can u interpret the intercept of your equation in words in the context of this problem. Does interpreting the intercept make sense in the problem? Explain.
Interpret the intercept of your equation in words in the context of this problem. Does interpreting the intercept makes sense in this problem? Explain.
If they mean to interpret where the line intercepts the x or y axis, the answer is it doesn't. Usually x,y intercepts are when you set x then y equal to zero to come up with where the intersect, however, since the total cost (TC or y) is never 0, (since you can't have 0 cuts), both x and y axis do not touch the "line". If they want to make (0,0) the first "point" of the line, you could say zero cuts = zero total cost, other than that, there are no x or y intercepts. Let me give you an example of regular line:
y = x + 3
Slope = 1
Constant = 3
x intercept (0,3) when x=0, y = 3 (line crosses x axis)
y intercept (-3,0) when x = -3, y = 0 (line crosses y axis)
Points on this line would included (including the intercepts above):
When you plot these 5 points, you will see the line is straight, slope is positive (inclining), line passes through x axis at x= -3 and passes through the y axis at y=3.
If you would like, I could graph the "line" for you and scan it into my computer and try to upload it to you. I could also give you the above graph so you can see the difference, how would that be?
Here is the graph of the scanned graph of TC = (0.25)(C-1) + 2.25Total Cost vs Cost per cut Graph.jpg
y = x + 3 graph attached ("normal line") X intercept = -3, y intercept = 3. Slope = 1, Points on line (-1, 2) (0.3), (1, 4), (-3, 0). Let me know if you have any other questions about the two graphs.y equals x plus 3 graph with x y intercepts and slope indicated.jpg
I went to nursing school so I know biology, a little chemistry, anatomy & physiology was my best subject. I can't do physics, never had the subject. But general science I am usually OK with.
Look up my name Beth L, or under Mathematics, Algebra subjects. You will see my name there. I am usually online from 5 or 6pm (eastern time, USA, North Carolina) to around 8 or 9pm unless I have a lot of students wanting my help, in that case, I am online until they are done asking me everything they need help.
FYI I have a Bachelor's degree (4 year) in Mathematics from Penn State University with over 20 years experience (graduated in 1995) in teaching/tutoring math (mostly algebra and geometry).
Yes I'll be online tomorrow night and the rest of the week from about 5 or 6pm eastern time to around 8 or 9pm. Sometimes I'm online much later, depends on how many students I am helping in one night. Sometimes I am still online at 10 or 11pm.
Anytime. Glad I could help you. Use those graphs I put up to help you to understand graphs.
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