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?\no y = 0.605x + 0.004\no y = 0.959x + 0.041\no y = 1.518x + 0.995\no y = 1.967x + 0.984

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?\no y = 0.605x + 0.004\no y = 0.959x + 0.041\no y = 1.518x + 0.995\no y = 1.967x + 0.984

Answer

Explanation:

Step1: Recall linear - regression concept

We want to find the best - fit line of the form $y = mx + b$ for the given data points $(x,y)$ where $x$ is the width and $y$ is the length of the rectangle. One way is to use a calculator or software with linear - regression functionality. Another way is to check each equation by substituting some of the data points. Let's take the first data point $(x = 6.1,y = 12.0)$.

Step2: Test the first equation

For $y=0.605x + 0.004$, when $x = 6.1$, $y=0.605\times6.1+0.004=3.6905 + 0.004=3.6945\neq12.0$.

Step3: Test the second equation

For $y = 0.959x+0.041$, when $x = 6.1$, $y=0.959\times6.1 + 0.041=5.8499+0.041 = 5.8909\neq12.0$.

Step4: Test the third equation

For $y=1.518x + 0.995$, when $x = 6.1$, $y=1.518\times6.1+0.995=9.2598 + 0.995=10.2548$. When $x = 5.0$, $y=1.518\times5.0+0.995=7.59+0.995 = 8.585\approx8.1$.

Step5: Test the fourth equation

For $y = 1.967x+0.904$, when $x = 6.1$, $y=1.967\times6.1+0.904=12.0987+0.904=13.0027\neq12.0$.

Answer:

$y = 1.518x+0.995$