To identify a coordinate that is a solution to the inequality \( 4x - 3y > 6 \), we can first rewrite the inequality in slope-intercept form (y = mx + b) to help us visualize it.
Starting with the inequality:
\[ 4x - 3y > 6 \]
We can rearrange it:
\[ -3y > -4x + 6 \]
Now, divide by -3 (remember that the inequality sign flips when you divide by a negative number):
\[ y < \frac{4}{3}x - 2 \]
This inequality defines a region below the line \( y = \frac{4}{3}x - 2 \).
To find a coordinate that is a solution, we can test an arbitrary point below this line. A good starting point is to test the origin (0,0):
Substituting \( x = 0 \) and \( y = 0 \) into the original inequality:
\[ 4(0) - 3(0) > 6 \]
This simplifies to:
\[ 0 > 6 \]
This statement is false, so the origin is not a solution.
Next, let's try the point (0, -3):
Substituting \( x = 0 \) and \( y = -3 \):
\[ 4(0) - 3(-3) > 6 \] \[ 0 + 9 > 6 \]
This statement is true, so the point \( (0, -3) \) is a solution to the inequality.
Therefore, a coordinate that is a solution to the inequality \( 4x - 3y > 6 \) is \( (0, -3) \).