Final answer:
The equation of the line passing through the points (-6, 4) and (-2, 2) is found to be y = -1/2x + 1 after calculating the slope as -1/2 and the y-intercept as 1. None of the provided options match this equation.
Step-by-step explanation:
To find the equation of a line that passes through the points (-6, 4) and (-2, 2), we first need to calculate the slope of the line using the formula:
m = (y2 - y1) / (x2 - x1)
For our points, (x1, y1) = (-6, 4) and (x2, y2) = (-2, 2), so:
m = (2 - 4) / (-2 + 6) = -2 / 4 = -1/2
Now that we have the slope, we use one of the points to find the y-intercept (b) using y = mx + b:
4 = (-1/2)(-6) + b
b = 4 - 3 = 1
Therefore, the equation of the line is y = -1/2x + 1, which is not one of the options provided in the question, suggesting a possible typo. In case of a typo, we should look for an option closest to our calculated equation. None of the options provided match our calculations, thus we cannot confidently select any of the given options.