Question

Nariah Rich Date Thinking With Mathematical test (continued ) Would a correlation coefficient for the variables of the Recycling Project be closest to -1,-0.5,0,0.5, or 1 ? Explain your choice. Use the points (200,100) and (50,25) to find an equation in the form y=mx+b for the modeling line. Show your work.

Answer 1

The correlation coefficient for the variables of the Recycling Project would be closest to -1, indicating a perfect negative linear relationship. The equation of the modeling line for the given points is y = 0.5x.

Step-by-step explanation:

The correlation coefficient for the variables of the Recycling Project would be closest to -1. A correlation coefficient of -1 indicates a perfect negative linear relationship between the variables. This means that as one variable increases, the other variable decreases in a predictable manner.

To find the equation of the modeling line using the points (200,100) and (50,25), we can use the slope formula:

slope (m) = (change in y) / (change in x) = (100 - 25) / (200 - 50) = 75 / 150 = 0.5

Using the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is a point on the line, we can choose either of the given points to substitute into the equation. Let's use (200,100):

y - 100 = 0.5(x - 200)

y - 100 = 0.5x - 100

y = 0.5x

So, the equation in the form y = mx + b for the modeling line is y = 0.5x.