Question

39. Kate recorded the time it took six children of

different ages to run one lap around the track.
Write an equation for the line of best fit, then
estimate the length of time it would take for her
5-year old brother to run one lap.
Age (yrs) Time (s)
9
180
137
12
126
12
124
102
11
15
16
78

Answer 1

`y=-11x+261`

Explanation:

As you can observe in the image attached, the line that best fits passes through point B and C. That means we can use those point to find the slope of such line.

`m=(y_(2) -y_(1) )/(x_(2)-x_(1) )`

Where
`B(11,137)` and
`C(12,126)`

`m=(126-137)/(12-11)=-11`

So, the slope of the line that best fits is -11, approximately.

Now, we use the point-slope formula to find the equation.

`y-y_(1) =m(x-x_(1) )\\y-137=-11(x-11)\\y=-11x+124+137\\y=-11x +261`

Therefore, the line that best fits is
`y=-11x+261` approximately.

Remember, when we estimate a line for some data on a scatterplot, we are calculating an approximation, that's why we also said "approximately", because the line is an approximation where the majority of point meet.