|
Question 1124438: Hello, I need help, please.
Tim is buying snacks for the Mathletes, who love microwave popcorn. When Tim looks at the popcorn selection he notices many brands and different prices. He wonders if the cost is related to the quality of the popcorn. To answer his question, he purchases a random sample of popcorn bags and records their price. When it is time for the Mathletes meeting he pops each bag in the same microwave, opens each bag, and counts the number of unpopped kernels.
Price ($) 2.30 0.60 1.30 1.50 1.70 1.00
# Unpopped 4 30 17 21 15 20
1. Make a scatterplot on graph paper and draw the line of best fit. Choose two points on your drawn line and use them to determine the equation of the line of best fit. What do the slope and the y-intercept represent in your equation?
2. Estimate the number of unpopped kernels (after cooking) in a bag that costs $1.19.
Thank you.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i plotted the points as instructed.
the coordinate points are in (x,y) format.
the points plotted are:
price 2.3 0.6 1.30 1.50 1.70 1.00
not popped 4 30 17 1 15 20
here they are in (x,y) format.
x is the price.
y is the number of kernels of corn that were not popped.
(x,y)
--------
(2.3, 4)
(.6, 30)
(1.3, 17)
(1.5,21)
(1.7,15)
(1,20)
i then drew a line of best fit as best i could.
the line of best fit is the line that minimizes the distance from each point to the line.
i picked 2 points to create this line.
those points were (.3,32) and (2.9,-2).
using these 2 points, i created the equation for this line.
that equation is y = -13.07692308 * x + 35.92307692.
i then used this equation to determine the value of y when x = 1.19.
that value of y was calculated to be 20.36153846.
on the graph, the value of y when x = 1.19 is shown as the point (x,y) = (1.19,20.362).
here's my graph.
the graphing software i used is at https://www.desmos.com/calculator
i plotted the points using the table function of that graphing software.
i looked at the graph and determined my line of best fit would go through the points (.3,32) and (2.9,-2)
the slope intercept form of the equation of a line is y = mx + x
m is the lsope
b is the y-intercept
i created the formula for the line using those 2 points.
i assigned (x1,y1) = (.3,32) and (x2,y2) = 2.9,-2)
the formula for the slope (y2 - y1) / (x2 - x1)
using that formula, i determined the slope of the line is equal to -13.07692308.
the equation became y = -13.07692308 * x + b
i then used one of the points to determine the y-intercept.
i used the point (2.9,-2) and replaced y with -2 and x with 2.9.
the equation of y = -13.07692308 * x + b became -2 = -13.07692308 * 2.9 + b
i solve for b to get b = -2 + 13.07692308 * 2.9.
this resulted in b = 35.92307692.
the equation of my line of best fit became:
y = -13.07692308 * x + 35.92307692
that't the line you see on the graph.
i then drew a vertical line at x = 1.19 to show the intersection of that line with the line of best fit.
that intersection is at (1.19,20.362).
that tells you the value of y is 20.362 when the value of x is 1.19.
in terms of the problem, it's telling you that you can expect approximately 20 kernels of corn to not be popped if you buy a bag of popcorn at a price of 1.19 per bag.
|
|
|
| |
