Final answer:
The standard form of the equation of the line passing through (-3, 5) and (2, -5) is 2x + 3y = 1.
Step-by-step explanation:
To find the standard form of the equation of a line that passes through two given points, (-3, 5) and (2, -5), we can use the point-slope form of the equation: y - y1 = m(x - x1). First, calculate the slope (m) using the formula m = (y2 - y1) / (x2 - x1). Substituting the coordinates, we get m = (-5 - 5) / (2 - (-3)) = -10 / 5 = -2. Next, choose one of the points (let's use (-3, 5)) and substitute the values into the point-slope equation: y - 5 = -2(x - (-3)). Simplify the equation to: y - 5 = -2(x + 3). Finally, convert the equation to standard form by expanding and rearranging the terms: 2x + 3y = 1. Therefore, the standard form of the equation of the line is 2x + 3y = 1 (option A).