Step-by-step Explanation:
Part A: Algebraically write the equation of the best fit line in slope-intercept form. Include all of your calculations in your final answer.
Considering the data
Age (in years) Weight (in pounds)
2 32
6 47
7 51
4 40
5 43
3 38
8 60
1 23
Considering the slope intercept form
[tex]y = mx + b[/tex]
where [tex]m[/tex] is the slope of the line and [tex]b[/tex] is the y-intercept.
Taking two points, lets say (2, 32) and (8, 60)
as
[tex]\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(2,\:32\right),\:\left(x_2,\:y_2\right)=\left(8,\:60\right)[/tex]
[tex]m=\frac{60-32}{8-2}[/tex]
[tex]m=\frac{14}{3}[/tex]
so
[tex]y = mx + b[/tex]
[tex]\:\:32\:=\:\left(\frac{14}{3}\right)2\:+\:b[/tex]
[tex]\mathrm{Switch\:sides}[/tex]
[tex]\left(\frac{14}{3}\right)\cdot \:2+b=32[/tex]
[tex]b=\frac{68}{3}[/tex]
Thus
[tex]y = mx + b[/tex]
as
[tex]m=\frac{14}{3}[/tex] and [tex]b=\frac{68}{3}[/tex]
substituting in the slop-intercept form
[tex]y=\left(\frac{14}{3}\right)x+\left(\frac{68}{3}\right)[/tex]
Therefore, [tex]y=\left(\frac{14}{3}\right)x+\left(\frac{68}{3}\right)[/tex] is the equation of the best fit line in slope-intercept form.
Part B: Use the equation for the line of best fit to approximate the weight of the little girl at an age of 14 years old.
As the equation of line is
[tex]y=\left(\frac{14}{3}\right)x+\left(\frac{68}{3}\right)[/tex]
So in order to find the weight of the little girl at an age of 14 years old, put
[tex]x = 14[/tex] in the above equation.
as
[tex]y=\left(\frac{14}{3}\right)x+\left(\frac{68}{3}\right)[/tex]
[tex]y=\left(\frac{14}{3}\right)\left(14\right)+\left(\frac{68}{3}\right)[/tex] ∵ [tex]x = 14[/tex]
[tex]\:y=88[/tex]
Therefore, the approximate weight of the little girl at an age of 14 years old will be 88 pounds.
Answer: Copy and Paste Version
Step-by-step explanation:
Y = mx + b
Taking two points (2,32) (8,60)
Slope between the 2 points is y2 - y1/x2 - x1
(x1,y1) (2,32) , (x2 - y2) (8,60)
m = 60 - 32/ 8 - 2
m = 14/3
y= mx + b
32 = (14/3) 2 + B
(14/3) times 2 + b = 32
b = 68/3
substituting in the slop-intercept form: y = (14/3) x + 68/3
Part B:
As the equation of line is
y = (14/3) x + 68/3
We have to put
X = 14 in the above equation.
y = (14/3) (14) + (68/3)
Y = 88 lbs
