Final answer:
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.