Question

What is the equation for the linear model in the scatter plot obtained by choosing the two points closest to the line? The two closest points are (35,32) and (45,48).

A. y = 1.6x - 24
B. y = 0.625x +10.125
C. y = - 1.6x - 24
D. y = 0.625x - 24.

Answer 1

To find the equation of the linear model, calculate the slope using the two provided points and then use one point to solve for the y-intercept. The correct equation, in this case, is A. y = 1.6x - 24.

Step-by-step explanation:

The question asks for the equation of the linear model based on two points on a scatter plot. To find the slope (m) of the line, use the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the given points. Substituting the points (35,32) and (45,48), the slope is (48-32)/(45-35), which is 16/10 or 1.6. The slope is part of the line's equation in the form y = mx + b.

Next, to find the y-intercept (b), use either point with the slope in the equation y = mx + b. Using the point (35,32), the equation becomes 32 = 1.6(35) + b. After solving, b = 32 - 56, which is -24. The equation of the line is then y = 1.6x - 24.

Therefore, the correct answer is A. y = 1.6x - 24.