To find the equation that represents the approximate line of best fit for the given data, we'll use the least-squares regression method. The regression line can be represented by the equation [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the intercept.
Given the data points:
- Font Sizes ([tex]\( x \)[/tex]): 14, 12, 16, 10, 12, 14, 16, 18, 24, 22
- Word Counts ([tex]\( y \)[/tex]): 352, 461, 340, 407, 435, 381, 280, 201, 138, 114
After calculating the line of best fit using the least-squares method, we find the slope [tex]\( m \)[/tex] and the intercept [tex]\( b \)[/tex]:
- The slope [tex]\( m \)[/tex] is approximately [tex]\( -26.059 \)[/tex]
- The intercept [tex]\( b \)[/tex] is approximately [tex]\( 722.633 \)[/tex]
Now, let us compare the given options with our calculated values:
1. [tex]\( y = -55x + 407 \)[/tex]
2. [tex]\( y = -41x + 814 \)[/tex]
3. [tex]\( y = -38x + 922 \)[/tex]
4. [tex]\( y = -26x + 723 \)[/tex]
The option that matches closest to our calculated line of best fit ([tex]\( y = -26.059x + 722.633 \)[/tex]) is clearly:
[tex]\( y = -26x + 723 \)[/tex]
Thus, the equation that best represents the approximate line of best fit for the data is:
[tex]\[ y = -26x + 723 \][/tex]
