a What is a line of best fit? What are two convenient points to choose?
B
b Use the line of best fit found in Part A.
A
aExample Graph:
Example Equation: y=-12.5x+35
B
b Around 20 unpopped kernels.
Practice makes perfect
a Given the table below related to the popcorn Tim bought, we are asked to make a scatterplot. We will then draw the line of best fit and find its equation.
Price($)
2.30
0.60
1.30
1.50
1.70
1.00
#Unpopped
4
30
17
21
15
20
Let's start by plotting the points.
Recall that the line of best fit does not necessarily need to pass through the points, it just needs to represent the behavior of the data we have. We can choose two convenient points lying on the grid — let's use (0,35) and (2.40,5). Notice that there are infinitely many possible correct solutions, and this is just one possibility.
Now we will find the equation for our line of best fit. Recall the slope-intercept form of a line.
y=mx+b
Here m is the slope of the line and b is the y-intercept. From our choice of points when we traced the line, we can identify the y-intercept as b=35. We can find the slope using the Slope Formula.
m = y_2-y_1/x_2-x_1
Here m is the slope and (x_1,y_2) and (x_2,y_2) are two known points. If we use the points we chose to trace our line we can calculate the slope of our linear function.
Now that we found the slope and the y-intercept we can write the equation for the line of best fit.
y=-12.5x+35.
b Now we need to estimate the number of unpopped kernels for a bag that costs $1.19. For this we will use the equation found in Part A and evaluate it at x=1.19.
Since the number needs to be an integer, our estimation for the number of unpopped kernels is 20. Once again, this is just one of the infinitely many possibilities of answers. However, other lines of best fit should predict values close to 20 as well.
