Final answer:
The equation of the line passing through the points (10,-5) and (-3,-5) is y = -5, as the line is horizontal with a slope of 0.
Step-by-step explanation:
The question is asking for the equation of the line that passes through the points (10,-5) and (-3,-5). To find the equation of a line, we need two things: the slope and a point through which the line passes. First, we determine the slope. The slope formula is (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. Using the points (10, -5) and (-3, -5), we find that the slope (m) is ( -5 - (-5) ) / ( -3 - 10), which simplifies to 0 / -13. This gives us a slope of 0, which means the line is horizontal.
Since the line is horizontal with a slope of 0, the equation of the line must be of the form y = b, where b is the y-coordinate that the line passes through. In this case, b = -5. Therefore, the equation of the line through the points (10,-5) and (-3,-5) is y = -5.