Final answer:
The equation of the line passing through the points (3, 1) and (-1, -7) is y = 2x - 5.
Step-by-step explanation:
The equation of the line passing through the points (3, 1) and (-1, -7) can be found using the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
To calculate the slope (m), we can use the formula (y2 - y1) / (x2 - x1). The coordinates (x1, y1) are (3, 1) and (x2, y2) are (-1, -7). Plugging these values in, we get (-7 - 1) / (-1 - 3) = -8 / -4 = 2.
Now that we have the slope, we can substitute the coordinates of one of the points into the equation y = mx + b and solve for b. Using the coordinates (3, 1), we get 1 = 2(3) + b. Simplifying this equation, we find b = -5.
Therefore, the equation of the line passing through the points (3, 1) and (-1, -7) is y = 2x - 5. Hence, the correct answer is A) y = 2x - 5.