To solve the linear inequality y < 4x + 5, we want to determine the set of all points (x, y) that satisfies this condition.
First, we can interpret this inequality graphically. The equation y = 4x + 5 represents a straight line in the coordinate system. The slope of this line is 4, which means for every 1 unit you move to the right (increasing x), the value of y increases by 4 units. The y-intercept is 5, meaning the line crosses the y-axis at (0, 5).
Since we are dealing with a less than inequality (<), the solution will be the area below the line. To visualize this, you can graph the line y = 4x + 5 and shade the region below it. This shaded area represents all the points (x, y) where y is less than 4x + 5.
Additionally, the line itself, y = 4x + 5, is not included in the solution set, since the inequality is strict (i.e., it does not include equal to). Therefore, any point on this line does not satisfy the inequality.
To find specific points that satisfy the inequality, you may choose any value for x and calculate the corresponding y value using the inequality. For example, if you choose x = 0, the inequality states that y can be any value less than 5. So, a possible solution could be the point (0, 4).
Thus, the set of solutions to the inequality y < 4x + 5 is all the points located in the region below the line in the graph.