lamoyne needs four pieces of lumber for his scout project. The pieces can be cut from one large piece of lumber according to the following pattern. The lumberyards will make the cuts for lamoyne at a fixed cost of 2.25 plus an additional cost of 25 cent per cut. One cut is free. What is the functional relationship between the total cost of cutting a piece of lumber and the number of cuts required? What is the equation of this function? Be sure to define variables in the context
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.
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.
Apr 7th, 2015
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?
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.
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.
Apr 8th, 2015
Anytime. Glad I could help you. Use those graphs I put up to help you to understand graphs.
Apr 8th, 2015
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