Question

In the graph for the solution set of the inequality 4x−3y>6 , identify the coordinate that is a solution

Answer 1

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 \( (0, -3) \).