ATry to draw a line that this very close to most of the data points.
BChoose two points that are on the line of best fit from Part A. Then, substitute their coordinates into the slope formula.
AExample Line of Best Fit:
BExample Equation: y=0.22x+4.2 Example Conjecture: The price of a ticket in 2020 will be about 9.7 dollars.
Practice makes perfect
We are given a scatter plot which shows the average ticket prices since 1995.
We are asked to draw a line that best represents the data in the scatter plot. Let's do it! We will try to draw a line so that it is as close to the points as possible.
This is only an example of a line of best fit. Other lines that are close to the points would also be correct.
In Part A, we drew a line that best represents the data in the scatter plot.
We are asked to write an equation in slope-intercept form of this line.
y=mx+bIn this equation, m is the slope and b is the y-intercept. To find the slope m, we will first identify the coordinates of two points that the line is passing through.
The first point that we chose has coordinates x_1= 8 and y_1= 6. The second point has coordinates x_2= 17 and y_2= 8. Let's substitute these values into slope formula.
We found that the slope m is equal to about 0.22. This means that the price of a ticket increased by 0.22 dollars each year.
y=mx+b ⇔ y= 0.22x+b
Now we will find the y-intercept b, which is the y-value when x=0. We can find it on the graph!
We can see that when x=0, the y-value is equal to about 4.2. Therefore, the y-intercept b is also equal to about 4.2.
y=0.22x+b ⇕ y=0.22x+ 4.2
We found the equation of the line of best fit in slope-intercept form! Now we can make a conjecture about the cost of a movie ticket in 2020. In our equation, y represents the ticket price and x represents the number of years since 1995. To make predictions about the ticket price in 2020, we first need to find the number of years between 1995 and 2020.
x=2020-1995 ⇔ x=25
Now we can substitute x=25 into the equation.
