darius is studying the relationship between mathematics and art. he asks friends to each draw a \typical\…

darius is studying the relationship between mathematics and art. he asks friends to each draw a \typical\ rectangle. he measures the length and width in centimeters of each rectangle and plots the points on a graph, where x represents the width and y represents the length. the points representing the rectangles are (6.1, 12.0), (5.0, 8.1), (9.1, 15.2), (6.5, 10.2), (7.4, 11.3), and (10.9, 17.5). which equation could darius use to determine the length, in centimeters, of a \typical\ rectangle for a given width in centimeters?\n y = 0.605x + 0.004\n y = 0.959x + 0.041\n y = 1.519x + 0.995\n y = 1.067x + 0.904

darius is studying the relationship between mathematics and art. he asks friends to each draw a \typical\ rectangle. he measures the length and width in centimeters of each rectangle and plots the points on a graph, where x represents the width and y represents the length. the points representing the rectangles are (6.1, 12.0), (5.0, 8.1), (9.1, 15.2), (6.5, 10.2), (7.4, 11.3), and (10.9, 17.5). which equation could darius use to determine the length, in centimeters, of a \typical\ rectangle for a given width in centimeters?\n y = 0.605x + 0.004\n y = 0.959x + 0.041\n y = 1.519x + 0.995\n y = 1.067x + 0.904

Answer

Explanation:

Step1: Calculate mean of x and y

x̄=45.0/6=7.5, ȳ=74.3/6≈12.383

Step2: Compute Σ(xy) and Σ(x²)

Σ(xy)=592.69, Σ(x²)=360.84

Step3: Calculate slope m

m=(6592.69 - 45.074.3)/(6*360.84 - 45.0²)=212.64/140.04≈1.518

Step4: Calculate intercept b

b≈12.383 - 1.518*7.5≈0.998≈0.995

Answer:

C. y = 1.518x + 0.995