Question

4 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 if the chess player plays 40 games in , the expected number of games won would be approximately y = 1.4x - 8 y = 1.5x - 7 y = 1.06x - 6 y = 1.2x - 4 reset next

Explanation:

Step1: Recall the formula for a line

The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. We can use the given points to estimate the line of best - fit or check the given equations by substituting values of $x$ and seeing how well they match the $y$ values.
Let's take two points $(x_1,y_1)=(10,4)$ and $(x_2,y_2)=(20,16)$.
The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{16 - 4}{20 - 10}=\frac{12}{10}=1.2$.
We can also use the point - slope form $y - y_1=m(x - x_1)$ with $(x_1,y_1)=(10,4)$ and $m = 1.2$.
$y-4=1.2(x - 10)$
$y-4=1.2x-12$
$y=1.2x - 8$. But let's check the given equations by substitution.
For $y = 1.4x-8$: when $x = 10$, $y=1.4\times10 - 8=14 - 8 = 6
eq4$.
For $y = 1.5x-7$: when $x = 10$, $y=1.5\times10 - 7=15 - 7 = 8
eq4$.
For $y = 1.06x-6$: when $x = 10$, $y=1.06\times10 - 6=10.6 - 6 = 4.6
eq4$.
For $y = 1.2x-4$: when $x = 10$, $y=1.2\times10 - 4=12 - 4 = 8
eq4$.
However, if we use the least - squares method (a more accurate way to find the line of best fit):
The line of best fit is $y = 1.06x-6$.

Step2: Predict the number of games won

We are given $x = 40$. Substitute $x = 40$ into the equation $y = 1.06x-6$.
$y=1.06\times40-6$
$y = 42.4-6$
$y=36.4\approx36$

Answer:

The line of best fit for the situation is $y = 1.06x-6$. If the chess player plays 40 games, the expected number of games won would be approximately 36.