Final answer:
The equation of the line passing through the points (0, -2) and (4, 10) is y = 3x - 2.
Step-by-step explanation:
The equation of a line in slope-intercept form is given by y = mx + b, where m represents the slope of the line and b represents the y-intercept. To find the equation of the line passing through the points (0, -2) and (4, 10), we can first calculate the slope (m) of the line using the formula: m = (y2 - y1)/(x2 - x1). In this case, the slope is (10 - (-2))/(4 - 0) = 12/4 = 3. Thus, the equation of the line is y = 3x + b. To find the value of b, we can substitute the coordinates of one of the points into the equation. Let's use the first point (0, -2). Substituting these values and solving for b, we get -2 = 3(0) + b. Simplifying, we find b = -2. Therefore, the equation of the line passing through the given points is y = 3x - 2, which corresponds to option A.