Final answer:
The equation of the line passing through the points (2, 3) and (0, -1) is determined by first calculating the slope and then using the point-slope form. The correct equation is y = 2x - 1.
Step-by-step explanation:
The question asks for the equation of the line that passes through the points (2, 3) and (0, -1). To find this, we first calculate the slope (m) using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. Plugging in the values, we get m = (-1 - 3) / (0 - 2) = -4 / -2 = 2.
Now that we have the slope, we can use the point-slope form, y - y1 = m(x - x1), to write the equation of the line. Substituting one of the points, say (2, 3), and the slope into the formula gives us y - 3 = 2(x - 2). Simplifying this, we get y = 2x - 4 + 3, which simplifies further to y = 2x - 1.
Thus, the correct equation of the line is y = 2x - 1, which matches with option C in the question provided.