To determine which equation represents the approximate line of best fit given the data in the table, we need to find the relationship between the font size (x) and the number of words per page (y). The line of best fit has the form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
From the analysis of the data provided:
- The slope [tex]\( m \)[/tex] is approximately [tex]\(-26\)[/tex]. This means that for every increase in font size by 1 unit, the number of words per page decreases by 26.
- The y-intercept [tex]\( b \)[/tex] is approximately [tex]\( 723 \)[/tex]. This represents the number of words that would fit on a page if the font size were zero.
Putting these values into the linear equation form, we get:
[tex]\[ y = -26x + 723 \][/tex]
Among the provided options:
- [tex]\( y = -55x + 407 \)[/tex]
- [tex]\( y = -41x + 814 \)[/tex]
- [tex]\( y = -38x + 922 \)[/tex]
- [tex]\( y = -26x + 723 \)[/tex]
The equation that represents the approximate line of best fit for the data is:
[tex]\[ y = -26x + 723 \][/tex]
So, the correct answer is:
[tex]\[ y = -26x + 723 \][/tex]
