Step-by-step explanation:
We have been given that Jeanie stated that the equation of this line best fit for the scatter plot is [tex]y=\frac{1}{2}x+8[/tex].
Let us find the slope of the line of best fit using points (2,7) and (4,6) in slope formula.
[tex]\text{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\text{Slope of line of best fit}=\frac{6-7}{4-2}[/tex]
[tex]\text{Slope of line of best fit}=\frac{-1}{2}[/tex]
We can see that slope of line of best fit is [tex]-\frac{1}{2}[/tex].
Since the equation of a line written in slope-intercept is in form: [tex]y=mx+b[/tex], where m=slope of line, b= y-intercept.
Upon substituting m=[tex]-\frac{1}{2}[/tex] and coordinates of one point in slope-intercept form of equation we will get,
[tex]6=-\frac{1}{2}\times 4+b[/tex]
[tex]6=-2+b[/tex]
[tex]6+2=-2+2+b[/tex]
[tex]8=b[/tex]
Upon substituting m=[tex]-\frac{1}{2}[/tex] and b=8 in slope intercept form, we will get,
[tex]y=-\frac{1}{2}x+8[/tex]
We can see that equation of the line of best fit is [tex]y=-\frac{1}{2}x+8[/tex]. Jeanie got 1/2 as slope of the line of best fit, which is wrong, therefore, Jeanie's equation of the line of best fit is not correct.
