Question

5
select the correct answer from each drop-down menu.
the table shows the number of games a chess player won in professional competitions, based on the number of games played.

games played (x)	10	15	20	25	30
games won (y)	4	10	16	21	25

the line of best fit for the situation is dropdown
if the chess player plays 40 games in competition, the expected number of games won would be approximately dropdown.
options for line of best fit: ( y = 1.2x - 4 ), ( y = 1.5x - 7 ), ( y = 1.4x - 8 ), ( y = 1.06x - 6 )

Explanation:

Step1: Verify line of best fit

Check each option with x values:
For \(x=10\): \(1.06(10)-6=4.6≈4\); \(1.2(10)-4=8≠4\); \(1.5(10)-7=8≠4\); \(1.4(10)-8=6≠4\). So best fit is \(y=1.06x-6\).

Step2: Predict for x=40

Substitute \(x=40\) into the line:
\(y=1.06(40)-6=42.4-6=36.4\)? Wait correction: Wait 1.0640=42.4 minus6=36.4? Wait no—wait 1.0640=42.4, 42.4-6=36.4? Wait the options may have 36 or 37, but according to calculation it's ~36.4≈36. But let's confirm:
Wait original data: x=10→y=4: 1.0610-6=4.6≈4; x=15→1.0615-6=15.9-6=9.9≈10; x=20→21.2-6=15.2≈16; x=25→26.5-6=20.5≈21; x=30→31.8-6=25.8≈26? Wait no original x=30→y=25: 25.8≈25, yes. So for x=40: 1.06*40-6=42.4-6=36.4≈36.

So the line of best fit is y=1.06x-6, expected games won≈36.

Wait the drop-down for line of best fit has y=1.06x-6 as an option, so that's correct. Then substituting x=40 gives ~36.

Final answer: line of best fit is y=1.06x-6, expected games won≈36.

Step1: Identify best fit line

Test \(x=10\): \(1.06(10)-6≈4\) (matches data).

Step2: Predict for x=40

Substitute \(x=40\): \(1.06(40)-6=36.4≈36\).

Answer:

y = 1.06x - 6; 38.4