Final answer:
To find the equation of the line through points (-5,-1) and (3,0), we calculate the slope as 1/8 and create the equation using point-slope form, yielding y = (1/8)x + (-3/8). However, this is not reflected in any of the provided answer options.
Step-by-step explanation:
To find the equation of the line that passes through the points (-5,-1) and (3,0), we must first calculate the slope (m) of the line using the slope formula m = (y2 - y1) / (x2 - x1). Plugging in the values, we get m = (0 - (-1)) / (3 - (-5)) = 1 / 8, which simplifies to m = 1 / 8. This is the slope of the line. Next, we use the point-slope form y - y1 = m(x - x1) to find the equation. Using the point (-5,-1) and the slope 1/8, the equation becomes y - (-1) = (1/8)(x - (-5)), which simplifies to y + 1 = (1/8)x + (5/8). Finally, to get the equation in y = mx + b form, we solve for y, yielding y = (1/8)x + (5/8) - 1, or equivalently, y = (1/8)x + (-3/8), after simplifying the constants.
None of the options A) y = -0.5x + 0.5, B) y = 0.5x - 0.5, C) y = -0.5x - 0.5, or D) y = 0.5x + 0.5 match the calculated equation y = (1/8)x + (-3/8). Thus, there may be an error in the question or in the provided options, as none correspond to the correct equation of the line through the given points.