Answer:
1)
[tex]y=\dfrac{1}{2}\times x+1[/tex] i.e. y = one half x + 1
2)
3, because y = negative one halfx + 9
Step-by-step explanation:
1)
It is given that the line of best fit of the scatter plot passes through the points (0,1) and (4,3).
so we will find the equation of line of best fit.
We know that the equation of line passing through two points (a,b) and (c,d) is calculated as:
[tex]y-b=\dfrac{d-b}{c-a}\times (x-a)[/tex]
Here we have:
(a,b)=(0,1) and (c,d)=(4,3).
Hence, the equation of line is:
[tex]y-1=\dfrac{3-1}{4-0}\times (x-0)\\\\y-1=\dfrac{2}{4}\times x\\\\y=\dfrac{1}{2}\times x+1[/tex]
Hence, the equation of this line of best fit in slope-intercept form is:
[tex]y=\dfrac{1}{2}\times x+1[/tex] i.e. y = one half x + 1
2)
It is given that the line of best fit crosses the y axis at 9 and passes through the point 6 and 6 i.e. it passes through (0,9) and (6,6).
so we will find the equation of line of best fit.
We know that the equation of line passing through two points (a,b) and (c,d) is calculated as:
[tex]y-b=\dfrac{d-b}{c-a}\times (x-a)[/tex]
Here we have:
(a,b)=(0,9) and (c,d)=(6,6).
Hence, the equation of line is:
[tex]y-9=\dfrac{6-9}{6-0}\times (x-0)\\\\y-9=\dfrac{-3}{6}\times x\\\\y=\dfrac{-1}{2}\times x+9[/tex]
Hence, the equation of this line of best fit in slope-intercept form is:
[tex]y=\dfrac{-1}{2}\times x+9[/tex]
Now we are asked to find the value of y when x=12.
[tex]y=\dfrac{-1}{2}\times 12+9\\\\y=-6+9\\\\y=3[/tex]
Hence, the correct answer is:
3, because y = negative one halfx + 9
