Answer:
The approximate equation of this line of best fit in slope-intercept form is:
[tex]y=\dfrac{-7}{5}\times x+14[/tex]
( i.e. option A is correct ; y = negative 7 over 5 x + 14 )
Step-by-step explanation:
Shannon drew the line of best fit on the scatter plot based on the information provided to us.
He observes that a straight line i.e. the line of best fit joins the ordered pairs (0,14) and (10,0).
Now we are asked to find the approximate equation of this line of best fit in slope-intercept form.
We know that the slope intercept form of a line is given by:
[tex]y=mx+c[/tex] where m denotes the slope of the line and c denote the y-intercept.
Also we know that the equation of a line passing through two points (a,b) and (c,d) is given by:
[tex]y-b=\dfrac{d-b}{c-a}\times (x-a)[/tex]
Here we have:
(a,b)=(0,14) and (c,d)=(10,0).
So equation of line is:
[tex]y-14=\dfrac{0-14}{10-0}\times (x-0)\\\\y-14=\dfrac{-14}{10}\times x\\\\y-14=\dfrac{-7}{5}\times x\\\\y=\dfrac{-7}{5}\times x+14[/tex]
Hence, the approximate equation of this line of best fit in slope-intercept form is:
[tex]y=\dfrac{-7}{5}\times x+14[/tex]
( i.e. option A is correct ; y = negative 7 over 5 x + 14 )
