Final answer:
The equation of the line passing through the points (-3, 5) and (3, -5) is y = (-5/3)x.
Step-by-step explanation:
The equation of a line passing through two given points can be found using the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept. To find the slope, we use the formula m = (y2 - y1) / (x2 - x1). Substitute the coordinates of the given points into the formula to find the slope. Then, substitute the slope and one of the points into the slope-intercept form to find the y-intercept. Finally, write the equation using the slope and y-intercept.
Using the points (-3, 5) and (3, -5), we find that the slope is -5 - 5 / 3 - (-3) = -10 / 6 = -5/3. Substituting the slope and the point (-3, 5) into the slope-intercept form, we get y = (-5/3)x + b. Substitute the coordinates of (-3, 5) into the equation to find the value of b. We get 5 = (-5/3)(-3) + b. Solving for b, we find that b = 0.
Therefore, the equation of the line that passes through the given points (-3, 5) and (3, -5) is y = (-5/3)x.