Final answer:
The equation of the line passing through (-1, -4) and (3, -2) is found using the slope formula and slope-intercept form of a line. After determining the slope to be 0.5 and rounding the y-intercept to -3, the equation is y = 0.5x - 3, which is option (a).
Step-by-step explanation:
To find the equation of the line passing through the points (-1, -4) and (3, -2), we need to determine the slope (m) and the y-intercept (b) of the line.
The slope is calculated using the formula m = (y2 - y1) / (x2 - x1). Plugging in our points, we get m = (-2 - (-4)) / (3 - (-1)) = 2 / 4 = 0.5. Now, we need to find the y-intercept.
Using the slope-intercept form, y = mx + b, we can substitute one of the points and the slope to solve for b. Let's use the point (-1, -4):
-4 = (0.5)(-1) + b
b = -4 + 0.5
b = -3.5
Since b must be a whole number in the answer choices, we round b to -3. Now we have the slope 0.5 and y-intercept -3, so the equation of the line is y = 0.5x - 3, which corresponds to option a).