Question

In the graph for the solution set of the inequality 4x−3y>6
, identify the coordinate that is a solution.(1 point)
Responses

(−2,0)
left parenthesis negative 2 comma 0 right parenthesis

(0,−2)
left parenthesis 0 comma negative 2 right parenthesis

(2,0)
left parenthesis 2 comma 0 right parenthesis

(0,2)

Answer 1

To determine which of the given coordinates is a solution to the inequality \( 4x - 3y > 6 \), we can test each point by substituting the \( x \) and \( y \) values into the inequality.

1. Testing the point \((-2, 0)\):
\[
4(-2) - 3(0) > 6 \implies -8 > 6 \quad \text{(false)}
\]

2. Testing the point \((0, -2)\):
\[
4(0) - 3(-2) > 6 \implies 0 + 6 > 6 \implies 6 > 6 \quad \text{(false)}
\]

3. Testing the point \((2, 0)\):
\[
4(2) - 3(0) > 6 \implies 8 > 6 \quad \text{(true)}
\]

4. Testing the point \((0, 2)\):
\[
4(0) - 3(2) > 6 \implies 0 - 6 > 6 \implies -6 > 6 \quad \text{(false)}
\]

The only coordinate that satisfies the inequality \( 4x - 3y > 6 \) is \((2, 0)\).

Thus, the answer is:

\((2, 0)\)