Find the slope of a line perpendicular to the line whose equation is 15, x, minus, 18, y, equals, minus, 48615x−18y=−486. Fully simplify your answer.
To find the slope of a line perpendicular to a given line, we need to determine the slope of the given line first.
The equation of the given line is 15x - 18y = -486.
We can rewrite this equation in the slope-intercept form (y = mx + b) by solving for y:
-18y = -15x - 486
Dividing both sides by -18, we get:
y = 15/18x + 27
The slope of the given line is therefore 15/18 or 5/6.
For a line to be perpendicular, its slope is the negative reciprocal of the original line's slope.
The negative reciprocal of 5/6 is -6/5.
Therefore, the slope of a line perpendicular to the given line is -6/5.