Question

2 multiple choice 4 points 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? $w = 60m + 3$ $w = 102m - 117$ $w = - 117m + 102$ $w = 3m + 60$

Explanation:

Step1: Substitute \(m = 2\) into each equation

• For \(w = 60m+3\): \(w=60\times2 + 3=120 + 3=123\)
• For \(w = 102m-117\): \(w=102\times2-117 = 204-117=87\)
• For \(w=-117m + 102\): \(w=-117\times2+102=-234 + 102=-132\)
• For \(w = 3m+60\): \(w=3\times2+60=6 + 60=66\)

Step2: Substitute \(m = 3\) into each equation

• For \(w = 60m+3\): \(w=60\times3+3=180+3 = 183\)
• For \(w = 102m-117\): \(w=102\times3-117=306-117 = 189\)
• For \(w=-117m + 102\): \(w=-117\times3+102=-351+102=-249\)
• For \(w = 3m+60\): \(w=3\times3+60=9+60=69\)

Step3: Analyze the closeness to the actual data

The actual data points are \((2,122)\), \((3,182)\).
The value of \(w = 60m + 3\) when \(m = 2\) is \(123\) (difference \(|123 - 122|=1\)), when \(m = 3\) is \(183\) (difference \(|183-182| = 1\)).
The other equations have larger differences from the actual data points for the given \(m\) values.

Answer:

\(w = 60m+3\)