Final answer:
The equation of the line passing through the points (-1,1) and (2,3) is calculated by first finding the slope, which is 2/3, and then using the point-slope form to arrive at the equation y = 2/3x + 5/3, option A.
Step-by-step explanation:
To find the equation of the line that passes through the points (-1,1) and (2,3), you first need to calculate the slope (m). The slope can be found using the formula m = (y2 - y1) / (x2 - x1). Plugging in our points, we get m = (3 - 1) / (2 - (-1)) = 2 / 3.
With the slope, we can then use the point-slope form of a line, y - y1 = m(x - x1), substituting one of our points and the slope into the formula. Using the point (-1,1), the equation becomes y - 1 = (2/3)(x + 1). Now, we just need to simplify and write it in the y = mx + b form, which gives us y = (2/3)x + (2/3) + 1 or y = (2/3)x + 5/3. Therefore, the correct answer is A. y = 2/3x + 5/3.