Question

Which quadrants does 2x-3y=24 pass through?

Answer 1

The line 2x-3y=24 passes through quadrants III and IV.

Step-by-step explanation:

The equation 2x-3y=24 represents a linear equation in two variables x and y. To determine which quadrants the line passes through, we can choose any x and y values and substitute them into the equation. If the resulting equation is true, then the point lies on the line.

Let's choose some values for x and y:

For x>0 and y>0, let's substitute x=2 and y=10: 2(2)-3(10)=24. This is false, so the line does not pass through quadrant I.

For x<0 and y>0, let's substitute x=-2 and y=10: 2(-2)-3(10)=24. This is false, so the line does not pass through quadrant II.

For x<0 and y<0, let's substitute x=-2 and y=-10: 2(-2)-3(-10)=24. This is true, so the line passes through quadrant III.

For x>0 and y<0, let's substitute x=2 and y=-10: 2(2)-3(-10)=24. This is true, so the line passes through quadrant IV.

Therefore, the line 2x-3y=24 passes through quadrants III and IV.