Question 41823This question is from textbook algebra an introductory course
: im not really sure if this is the right topic for my question.
NUMBER OF | | | | |
TICKETS(n) | 1 | 2 | 3 | 4 | 5
____________|_________| ________|________|________|_________
COST IN | 1.50 | 3.00 | 4.50 | 6.00 | 7.50
DOLLARS(c) | | | | |
WRITE A FORMULA TO EXPRESS THE RELATIONSHIP SHOWN IN EACH TABLE
IM NOT SURE HOW TO SOLVE THIS, PLEASE HELP ME
This question is from textbook algebra an introductory course
Found 2 solutions by psbhowmick, tutorcecilia:
Answer by psbhowmick(878)   (Show Source):
You can put this solution on YOUR website! Look, the difference between the prices of tickets of any two consecutive serial no. is 1.5.
So we can denote the price of the n-th ticket as $ .
If the absolute value (means only value irrespective of sign + or -) of difference between any two consecutive terms is constant in a series, then the series is called Arithmetic Series or Arithmetic Progression (A.P). The general form of an A.P. series upto n-terms is: a, a+d, a+2d, a+3d, ...... , a+(n-1)d. The first term is 'a' and the above mentioned difference is called common difference and is equal to 'd'. The n-th term of the series is 'a+(n-1)d'.
Answer by tutorcecilia(2152)  (Show Source):
You can put this solution on YOUR website! This problem involves the equation of a line. The formula is y = mx + b
y = any value for y
m = the slope of the line
x = any matching value for x
b = the point where the line crosses the y-axis.
In your table, the "x" values are "the number of tickets." The corresponding "y" values are the cost for that number of tickets.
For example 1 ticket costs $1.50. Two tickets cost $3.00, etc.
.
First, find the slope of the line using:
slope (m) = (y1 - y2)/(x1-x2)
I picked any two points from your table:
(1, 1.50) and (2, 3.00). The first number is the x value and the second number is the y value.
.
Slope = (1.50-3.00)/(1-2)= 1.5
.
Next plug in values for y = mx + b and solve for "b". I picked the point (2, 3.00) again
.
3.00= (1.50)2 + b
3.00 = 3.00 + b
3.00 - 3.00 = b
0 = b (which is the value for the y-intercept)
.
Plug-in the values that we found for the slope and the y-intercept values into the equation for the equation of the line:
y = 1.5x + 0
or
y = 1.5x
.
Check by testing another point from your table. Lets pick (4, 6.00)
6.00 = (1.5)(4) + 0
.
6 = 6
So what this table tells you is that for every ticket sold, the slope or price goes up $1.50. Using the slope-intercept formula helps to predict the cost of any number of tickets. The cost ("y") of 135 tickets ("x") at $1.50("m")would be:
y = (1.5)(135) + 0
y = $202.50
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