Find the slope of a line perpendicular to the line whose equation is x, plus, y, equals, 9x+y=9. Fully simplify your answer.
To find the slope of the line given by the equation 9x + y = 9, we need to rearrange the equation into the slope-intercept form, y = mx + b, where m is the slope of the line.
9x + y = 9
y = -9x + 9
So, the slope of the line given by the equation 9x + y = 9 is -9.
The slope of a line perpendicular to this line is the negative reciprocal of -9. The negative reciprocal of a number is found by taking the negative of the reciprocal of the number.
Reciprocal of -9 is -1/9.
The negative of -1/9 is 1/9.
Therefore, the slope of a line perpendicular to the line 9x + y = 9 is 1/9.