Final Answer:
Yes, the point (3, 8) satisfies the inequality \( y < 9x + 6 \).
Step-by-step explanation:
To verify if the point (3, 8) satisfies the given inequality, substitute the x and y coordinates of the point into the inequality and evaluate the expression. The inequality \( y < 9x + 6 \) can be rewritten as \( 8 < 9(3) + 6 \) since the point has coordinates (3, 8). Simplifying the right side gives \( 8 < 27 + 6 \). Further simplification yields \( 8 < 33 \), which is true. Therefore, the point (3, 8) satisfies the inequality.
Understanding this process is essential in determining whether a given point lies in the solution set of an inequality. It involves substituting the x and y values of the point into the inequality and evaluating the expression to check if the inequality holds true. In this case, the inequality is satisfied, indicating that the point (3, 8) is a valid solution.
This method is a fundamental approach in algebra and graphing, especially when dealing with linear inequalities. It allows for a systematic evaluation of points in relation to the inequality, aiding in the identification of regions that satisfy or do not satisfy the given conditions.