Teaneck High had an enrollment of 11050 in 1990 and an enrollment of 13390 in year 1998. What is the predicted enrollment of Teaneck High in 2018 if we assume a linear model?
The slope of the line is (13390-11050)/(1998-1990)
Use the same line to figure for 2018
To find the predicted enrollment of Teaneck High in 2018 using a linear model, we need to first determine the equation of the line that best represents the relationship between the year and the enrollment.
Step 1: Calculate the slope of the line.
The slope of a line is found using the formula: slope (m) = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line. In this case, we can use the points (1990, 11050) and (1998, 13390) to calculate the slope.
Slope (m) = (13390 - 11050) / (1998 - 1990)
= 2340 / 8
= 292.5
Step 2: Determine the equation of the line.
The equation of a line in slope-intercept form is given by: y = mx + b, where m represents the slope and b represents the y-intercept. To find the equation of the line, we substitute the slope and one of the given points into this equation.
Using the point (1990, 11050), we have:
11050 = 292.5 * 1990 + b
Solving for b:
b = 11050 - 292.5 * 1990
≈ -576185
Therefore, the equation of the line is:
y = 292.5x - 576185
Step 3: Substitute x = 2018 into the equation.
To find the predicted enrollment of Teaneck High in 2018, substitute x = 2018 into the equation:
y = 292.5 * 2018 - 576185
≈ 16528
Hence, the predicted enrollment of Teaneck High in 2018, assuming a linear model, is approximately 16528.
To predict the enrollment of Teaneck High in 2018 using a linear model, we need to find the equation of the line that represents the relationship between the year and enrollment.
Let's label the year as x and the enrollment as y.
We are given two data points:
- In 1990 (x=1990), the enrollment was 11050 (y=11050).
- In 1998 (x=1998), the enrollment was 13390 (y=13390).
We can use these two points to find the equation of the line using the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
First, let's calculate the slope (m):
m = (y2 - y1) / (x2 - x1)
= (13390 - 11050) / (1998 - 1990)
= 2340 / 8
= 292.5
Now, let's substitute one of the points and the slope into the equation to solve for b:
11050 = 292.5 * 1990 + b
11050 = 582075 + b
b = 11050 - 582075
b = -571025
Therefore, the equation of the line representing the enrollment of Teaneck High is y = 292.5x - 571025.
To predict the enrollment in 2018, we substitute x = 2018 into the equation:
y = 292.5 * 2018 - 571025
y = 589.5 - 571025
y = 13314.5
Therefore, the predicted enrollment of Teaneck High in 2018, assuming a linear model, is 13,314.5.