Complete Question:
The enrollment at East Valley High School over a six-year period is displayed in the scatterplot. Student Enrollment at East Valley High School (1st picture)
Which is the equation of the line of best-fit for this scatterplot? (2nd picture)
Answer:
D) y = (81/2)x - (160,069/2)
Step-by-step Explanation:
From the scatter plot in the graph attached below, we are given the ordered pairs of the coordinates (2009, 1330), (2013, 1492), we can derive the equation of the line of best-fit for the scatter plot using the slope-intercept formula.
Thus, the slope-intercept formula is y = mx + b, where m is the slope of the line; and b is the y-intercept.
We need to find m, and then b to input into the formula to get our equation of the line.
==> Finding m using the two sets of coordinate given on the graph [ (2009, 1330) and (2013, 1492) ]:
slope (m) = (y2 - y1)/(x2 - x1)
m = (1492 - 1330)/(2013 - 2009)
= 162/4
m = 81/2
Next is to find b, which is the y-intercept
Recall, y = mx + b
Using one of the coordinates given (2009, 1330), we can find b by inputting 1330 for y, 2009 for x, and 81/2 for m in the slope-intercept formula:
Thus, we would have ==>
1330 = (81/2 * 2009) + b
1330 = (162,729/2) + b
1330 - 162,729/2 = b
(2,660 - 162,729)/2 = b
- 160,069/2 = b
Having known the values of m, and b, let's input their values to get the equation of the line.
Thus, using the slope-intercept formula y = mx + b, the equation of the line of best-fit for the scatter plot would be
==> y = (81/2)x +(-160,069/2)
y = (81/2)x - (160,069/2)
