Final answer:
The equation of the line passing through the given points is y = 3x - 7.
Step-by-step explanation:
The equation of a line passing through two points can be found using the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
First, calculate the slope, m, using the formula: m = Δy / Δx, where Δy is the change in y-coordinates and Δx is the change in x-coordinates.
Given the points (2, -1) and (4, 5), the slope is (5 - (-1)) / (4 - 2) = 6 / 2 = 3.
Substitute one of the points and the slope into the slope-intercept form to find the y-intercept: -1 = 3(2) + b. Solving for b, we get b = -7.
Therefore, the equation of the line is y = 3x - 7. Option B, -3x + y = -7, matches the equation of the line.