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Which is the graph of the linear inequality y > -4/3x + 5?

Which is the graph of the linear inequality y > -4/3x + 5?-example-1
Which is the graph of the linear inequality y > -4/3x + 5?-example-1
Which is the graph of the linear inequality y > -4/3x + 5?-example-2
Which is the graph of the linear inequality y > -4/3x + 5?-example-3
Which is the graph of the linear inequality y > -4/3x + 5?-example-4

1 Answer

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The linear inequality
\(y > -(4)/(3)x + 5\) represents a half-plane above the line
\(y = -(4)/(3)x + 5\). Points in this shaded region satisfy the inequality, with the line itself not included due to the strict inequality (
\( > \)). Hence, graph 2 is correct.

The linear inequality
\(y > -(4)/(3)x + 5\) represents a half-plane above the line
\(y = -(4)/(3)x + 5\). The inequality indicates that any point (x, y) above the line satisfies the inequality.

The line itself is not included in the solution, as the inequality is strict (
\( > \)). The slope of the line is
\(-(4)/(3)\), meaning it goes downward from left to right.

The y-intercept is 5, and the line extends infinitely in both directions. Shading the area above the line represents the solution region for
\(y > -(4)/(3)x + 5\).

Any point in this shaded region, when substituted into the inequality, will result in a true statement, satisfying the inequality. The graph 2 given shows the linear inequality y > -4/3x + 5.

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