Final answer:
To find the equation of the line passing through the points (4, -2) and (6, 4), we calculated the slope to be 3 and used the point-slope form to arrive at the equation y = 3x - 14. Thus, the correct answer is B) y = 3x - 14.
Step-by-step explanation:
To find the equation of a line that passes through two points, we first calculate the slope of the line and then use one of the points to find the y-intercept. The slope (m) is determined by the change in y over the change in x, which is (y2-y1)/(x2-x1). Let's calculate the slope for the points (4, -2) and (6, 4):
m = (4 - (-2)) / (6 - 4) = 6 / 2 = 3.
Now that we have the slope, we can use the point-slope form of a line equation, y - y1 = m(x - x1), and one of the given points to find the equation. Let's use the point (4, -2):
y - (-2) = 3(x - 4)
y + 2 = 3x - 12
y = 3x - 14
The correct answer is B) y = 3x - 14.