The graph of the linear inequality y < 7x + 4 represents all the points in the coordinate plane that lie below the line defined by the equation y = 7x + 4. This line has a slope of 7 and a y-intercept of 4, meaning it crosses the y-axis at the point (0, 4).
To correctly represent the inequality on a graph, you would first draw the line for y = 7x + 4 as a dashed line, indicating that points on the line itself are not included in the solution set (since it’s a strict inequality ‘<'). The region below this line represents all the potential solutions to the inequality. Any point (x, y) that lies below the dashed line satisfies the condition that y is less than 7x + 4.
Thus, the description of this graph can be summarized as follows: the line is dashed and extends infinitely in both directions, while the shaded region below the line indicates where the solutions to the inequality are located.