To find the equation of a line passing through two points, we first need to find the slope of the line. The slope is given by the formula: (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two given points.
Using this formula, we find that the slope of the line passing through the points (-1, 0) and (3, -2) is (-2 - 0) / (3 - (-1)) = -2 / 4 = -0.5.
Next, we need to find the y-intercept of the line, which is the point where the line intersects the y-axis. We can find this by using the formula: y = mx + c, where m is the slope that we've just computed, x is the x-coordinate of one of the points, and y is the corresponding y-coordinate. By substitifying these values into the formula, we get: 0 = -0.5* -1 + c. From here, we can solve for c to get c = -0.5.
Therefore, the equation of the line that passes through the points (-1, 0) and (3, -2) is y = -0.5x - 0.5.