Final answer:
A graph of a linear equation forms a straight line representing all its solutions, while a graph of a linear inequality forms a half-plane, where the inequality's boundary line is shaded above or below depending on the direction of the inequality.
Step-by-step explanation:
Comparison of Linear Inequality and Linear Equation Graphs
A linear equation in two variables has the general form y = mx + b, where m represents the slope of the line and b is the y-intercept. This equation results in a straight line when graphed on a coordinate plane with perpendicular axes, where the x-axis is usually the independent variable and the y-axis is the dependent variable.
In contrast, a linear inequality such as y < mx + b or y > mx + b, will also graph as a line, but this line represents the boundary of a half-plane. The area above or below this line (depending on the inequality sign) will be shaded to indicate all the solutions to the inequality. The line itself may or may not be included in the solution set, indicated visually by using a dotted line (not included) or a solid line (included).
While both graphs involve a straight line, the key difference lies in representation. The line on a graph of a linear equation represents just the solutions to the equation, whereas the shaded region on a graph of a linear inequality represents all the solutions to the inequality.