The points A and B have coordinates (− 2,9) and (6,− 3) respectively. The line l  is the perpendicular bisector of AB.Find an equation for l in the form ax+by+c=0 , where a,b and c are integers.

Sure, here are the steps to find the equation of the line:

Step 1: Find the midpoint of AB. The midpoint M(x, y) of two points A(x1, y1) and B(x2, y2) is given by M = ((x1 + x2)/2, (y1 + y2)/2). So, the midpoint of A(-2, 9) and B(6, -3) is M = ((-2 + 6)/2, (9 - 3)/2) = (2, 3).

Step 2: Find the slope of AB. The slope of a line through points (x1, y1) and (x2, y2) is (y2 - y1) / (x2 - x1). So, the slope of AB is (-3 - 9) / (6 - (-2)) = -12 / 8 = -1.5.

Step 3: The slope of the line perpendicular to AB (line l) is the negative reciprocal of the slope of AB. So, the slope of line l is -1 / -1.5 = 2/3.

Step 4: Use the point-slope form of a line equation to find the equation of line l. The point-slope form is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Using the midpoint M(2, 3) and the slope 2/3, we get y - 3 = 2/3(x - 2).

Step 5: Convert the equation to the form ax + by + c = 0. First, multiply through by 3 to get rid of the fraction: 3y - 9 = 2x - 4. Then, rearrange to get 2x - 3y + 5 = 0.

So, the equation of the line l is 2x - 3y + 5 = 0.