Final answer:
The slope of the original line through points A(-3,1) and B(7,-3) is -2/5, so the slope of the perpendicular line is 5/2. Without a specific point on the perpendicular line, the equation can only be expressed as y = (5/2)x + b, where 'b' is the y-intercept to be determined.
Step-by-step explanation:
To find the equation of a line perpendicular to the line connecting the points A(-3,1) and B(7,-3), we first need to calculate the slope of the line connecting A and B. The slope (m) is defined as the change in the vertical axis (y) divided by the change in the horizontal axis (x), which in this case is (1 - (-3)) / (-3 - 7) = 4 / -10 = -2/5.
Since the slope of the perpendicular line is the negative reciprocal of the original line's slope, the perpendicular slope will be 5/2. To express this line in slope-intercept form (y = mx + b), we need a point through which the line passes to solve for 'b', the y-intercept. However, since a specific point is not given, we can only provide the slope-intercept form of the perpendicular line as y = (5/2)x + b, where 'b' will be determined when a specific point is known.