Find the slope of a line perpendicular to the line whose equation is 15, x, plus, 18, y, equals, 27015x+18y=270. Fully simplify your answer.

Answer 1

To find the slope of a line perpendicular to a given line, we can use the fact that perpendicular lines have slopes that are negative reciprocals of each other.

The equation of the given line is 15x + 18y = 270.

We can rewrite this equation in slope-intercept form (y = mx + b) by solving for y:
18y = -15x + 270
y = (-15/18)x + 270/18
y = -(5/6)x + 15

The slope of the given line is -5/6.

The slope of a line perpendicular to the given line will be a negative reciprocal of -5/6. The negative reciprocal of a fraction a/b is -b/a.

Therefore, the slope of a line perpendicular to the given line is -(-6/5), which simplifies to 6/5.

So, the slope of the line perpendicular to 15x + 18y = 270 is 6/5.