To determine the relationship between the width (x) and length (y) of a "typical" rectangle given the data points, we need to find the best-fit line equation of the form [tex]\( y = mx + c \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( c \)[/tex] is the y-intercept.
Given the points:
[tex]\[ (6.1, 12.0), (5.0, 8.1), (9.1, 15.2), (6.5, 10.2), (7.4, 11.3), (10.9, 17.5) \][/tex]
We find the best-fit line using linear regression. The resulting coefficients (slope [tex]\( m \)[/tex] and intercept [tex]\( c \)[/tex]) will give us the equation that best represents the data.
After performing the regression analysis, it is found that the slope [tex]\( m \)[/tex] and intercept [tex]\( c \)[/tex] of the line fitting these points match closely with one of the given options.
The calculations match the coefficients [tex]\( m = 1.518 \)[/tex] and [tex]\( c = 0.995 \)[/tex].
Therefore, the equation Darius could use to determine the length [tex]\( y \)[/tex] for a given width [tex]\( x \)[/tex] is:
[tex]\[ y = 1.518x + 0.995 \][/tex]
Thus, the correct equation is:
[tex]\[ y = 1.518 x + 0.995 \][/tex]
And the corresponding multiple-choice answer is:
[tex]\[ \text{Option: } \quad y = 1.518x + 0.995 \][/tex]
