Question

the table below shows the number of words a student typed during five timed sessions.
students typing
time (m)
(in minutes)
2
3
4
6
9
number of words typed (w)
122
182
240
368
538
which equation best models a line of best fit for these data?
w = -117m + 102
w = 60m + 3
w = 3m + 60
w = 102m - 117

Explanation:

Step1: Estimate slope from data

Choose two points, e.g., $(2,122)$ and $(9,538)$.
Slope $m_{slope} = \frac{538-122}{9-2} = \frac{416}{7} \approx 59.43 \approx 60$

Step2: Test intercept with slope

Use point $(2,122)$ and slope 60:
$122 = 60(2) + b$
$122 = 120 + b$
$b = 2 \approx 3$

Step3: Verify with other points

For $m=3$: $w=60(3)+3=183$, matches 182 closely.
For $m=4$: $w=60(4)+3=243$, matches 240 closely.

Answer:

$w = 60m + 3$