Question

What is the slope of the line determined by any two solutions to the equation $\frac{2}{x}+\frac{3}{y} = 0$? Express your answer as a common fraction.

Answer 1

To determine the slope, solve for y in terms of x, resulting in the equation y = (-3/2)x. Hence, the slope of the line described by the equation 2/x + 3/y = 0 is -3/2.

Step-by-step explanation:

To find the slope of the line determined by any two solutions to the equation 2/x + 3/y = 0, let's begin by solving for y in terms of x.

First, we isolate the term 3/y:

2/x = -3/y

Then we cross-multiply and get:

2y = -3x

Now we solve for y:

y = (-3/2)x

This is now in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. In this case, there is no y-intercept since the line passes through the origin.

The slope m is -3/2. So any two solutions to the original equation will yield a line with a slope of -3/2.

Answer 2

2x + 3y = 0
3y = -2x + 0
y = -2/3x + 0

the slope of this line is -2/3