It would be the negative of the negative reciprocal. And since the negative of a negative is a posivie, it is the positive reciprocal.. For example, if the slope was -3, the other would be 1/3.
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The negative reciprocal of any gradient gives the gradient of the line perpendicular to it. If you had a line of gradient 2, the negative reciprocal would be -1/2 Just change the sign on the number and flip the number/fraction to get the negative reciprocal.
A perpendicular lines slope is always the negative or opposite reciprocal of a lines slope. Therefore, if your slope is -13/1 then the perpendicularity of the other line is 1/13. The 13 would change positive there fore its its already a negative number then change it posiive.
The negative reciprocal of zero would be any undefined fraction. 0/x=0 negative reciprocal: -(x/0)= undefined.
The reciprocal of a number is 1 divide by that number - the reciprocal of -3 is 1/(-3), or -1/3. So, the negative reciprocal of -3 would be 1/3 (without the minus sign).
x - 3y = 9 can be rewritten in y = mx + b notation as y = x/3 - 3. The slope of this line (m) is 1/3. To find the slope of a perpindicular line, multiply m by negative one and take the reciprocal. So the slope of the new perpindicular line would be -3.