Find the slope of a line perpendicular to the line whose equation is 3, x, plus, y, equals, 83x+y=8. Fully simplify your answer.
To find the slope of a line perpendicular to the given line, we first need to find the slope of the given line.
The given line is in the form y = mx + b, where m is the slope of the line. To find the slope, we need to rearrange the equation into the slope-intercept form.
83x + y = 8
y = -83x + 8
So the slope of the given line is -83.
The slope of a line perpendicular to a line with slope m is the negative reciprocal of m. Therefore, the slope of a line perpendicular to the given line is the negative reciprocal of -83.
Let m be the slope of the perpendicular line, then we have:
m * (-83) = -1
m = -1 / (-83)
m = 1/83
Therefore, the slope of the line perpendicular to the given line is 1/83.