SOLUTION: Please help? I don;t understand the process of this. The following problem can be modeled with a linear equation. Analyze the problem and identify what quantities the variables

Algebra ->  Probability-and-statistics -> SOLUTION: Please help? I don;t understand the process of this. The following problem can be modeled with a linear equation. Analyze the problem and identify what quantities the variables      Log On


   

Question 478318: Please help? I don;t understand the process of this.
The following problem can be modeled with a linear equation. Analyze the problem and identify what quantities the variables x and y represent. The information provided in the problem is adequate to determine a point and a slope or two points on the line.
Robinson Wholesale Company paid $1380 for 500 items. Later they bought 800 items for $1710. Assume that the cost is a linear function of the number of items. Write the equation. (Let y represent the amount paid and x represent the number of items purchased.)
The answer is y = 1.1x + 830 I don't have a clue how to get this though.
???
Found 2 solutions by ankor@dixie-net.com, scott8148:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Robinson Wholesale Company paid $1380 for 500 items.
Later they bought 800 items for $1710.
Assume that the cost is a linear function of the number of items.
Write the equation.
(Let y represent the amount paid and x represent the number of items purchased.)
:
Assign the xy values as follows
x1=500; y1=1380
x2=800; y2=1710
:
Find the slope using the equation; m=%28y2-y1%29%2F%28x2-x1%29
:
m = %281710-1380%29%2F%28800-500%29
:
m = 330%2F300
m = 1.1 is the slope
:
Use the point/slope formula create the equation: y - y1 = m(x-x1)
y - 1380 = 1.1(x - 500)
y - 1380 = 1.1x - 550
y = 1.1x - 550 + 1380
y = 1.1x + 830
:'
Now do you see how they came up with this??

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
they got 300 more items (800 - 500) for 330 more $ (1710 - 1380)
___ this is a cost of $1.1 per item (330 / 300) ___ this piece price is the slope of the line

using either order, you can subtract the piece price and find the fixed costs
___ $830 for set up charges, delivery, etc. ___ this is the y-intercept of the line