The x-axis is the horizontal line on a coordinate plane that represents the independent variable. It is the horizontal reference line that intersects the origin (0,0) and extends infinitely in both the positive and negative directions.
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The x-axis is used to represent and graph linear equations, linear inequalities, and systems of linear equations.
The x-intercept of a line is the point where the graph of the line crosses the x-axis, representing the value of x when y = 0.
The equation of a line in slope-intercept form, $y = mx + b$, shows that the x-axis represents the independent variable x.
When graphing linear inequalities, the x-axis is used to determine the range of values for the independent variable x that satisfy the inequality.
In a system of linear equations, the x-axis is used to represent the independent variable x, which is solved for to find the point of intersection.
Review Questions
Explain the role of the x-axis in graphing linear equations.
The x-axis is the horizontal reference line on a coordinate plane that represents the independent variable, x. When graphing a linear equation in the form $y = mx + b$, the x-axis is used to plot the values of the independent variable x, while the y-axis is used to plot the corresponding values of the dependent variable y. The x-intercept of the line, where the graph crosses the x-axis, represents the value of x when y = 0.
Describe how the x-axis is used to graph linear inequalities.
When graphing a linear inequality, the x-axis is used to represent the range of values for the independent variable x that satisfy the inequality. The graph of the inequality is a half-plane, with the boundary line representing the equation of the inequality. The x-axis is used to determine the x-values that fall within the shaded region of the graph, which represents the solutions to the inequality.
Analyze the role of the x-axis in solving systems of linear equations by graphing.
In a system of linear equations, the x-axis is used to represent the independent variable x. By graphing the equations on the same coordinate plane, the point of intersection between the lines represents the solution to the system, where the values of both the x and y variables satisfy all the equations. The x-coordinate of the point of intersection corresponds to the value of the independent variable x that solves the system.