Final answer:
To find the standard equation of the line through points A (-3,5) and B (3,-5), we first find the slope using the coordinates of the points and the formula m = (y2-y1)/(x2-x1). Then, we use the point-slope formula y - y1 = m(x - x1) and plug in the values of one of the points to get the equation. Finally, we compare the equation with the choices to find the correct answer.
Step-by-step explanation:
To find the standard equation of the line through points A (-3,5) and B (3,-5), we first need to find the slope. The slope (m) between two points (x1, y1) and (x2, y2) is given by the formula m = (y2-y1)/(x2-x1). So, using the coordinates of points A and B, we have m = (-5-5)/(3-(-3)) = -10/6 = -5/3. With the slope found, we can use the point-slope formula y - y1 = m(x - x1) and plug in the values of point A to get the equation y - 5 = (-5/3)(x - (-3)). Simplifying this equation gives us the standard equation of the line as y = (-5/3)x + 10/3. Comparing this with the choices given, the correct answer is d) 3x - 5y = 0.