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The equation ( y = -x + 4 ) represents a linear boundary line in a two-dimensional coordinate plane. The inequality ( y < -x + 4 ) indicates that we are interested in the region below this line. The line itself is not included in the solution set, as indicated by the strict inequality, which distinguishes the boundary from the solutions. Thus, the boundary line serves as a critical demarcation for the area that satisfies the inequality.
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What inequality represents the graph?
To determine the inequality that represents a graph, you need to analyze its features, such as the shaded region and the boundary line. If the boundary line is solid, the inequality includes "≤" or "≥," while a dashed line indicates "<" or ">". The shaded region shows where the values satisfy the inequality. By identifying the slope and y-intercept of the line, you can formulate the correct inequality.
How do you describe the steps for graphing a two variable linear inequality?
To graph a two-variable linear inequality, first convert the inequality into an equation by replacing the inequality sign with an equal sign, which gives you the boundary line. Next, graph this line using a solid line for ≤ or ≥ and a dashed line for < or >. Then, determine which side of the line to shade by testing a point not on the line (usually the origin) to see if it satisfies the inequality. Finally, shade the appropriate region to represent all the solutions to the inequality.
What is the region of a coordinate plane that is described by a linear inequality?
The region of a coordinate plane described by a linear inequality consists of all the points that satisfy the inequality, which can be either above or below the boundary line defined by the corresponding linear equation. The boundary line itself is typically dashed if the inequality is strict (e.g., > or <) and solid if it is inclusive (e.g., ≥ or ≤). This region can be unbounded and may extend infinitely in one or more directions, depending on the specific inequality. The solution set includes all points (x, y) that make the inequality true.
Ask us graphing a linear inequality the first step is to replace the inequality symbol with a(n) sign.?
When graphing a linear inequality, the first step is to replace the inequality symbol with an equal sign to graph the corresponding linear equation. This creates a boundary line, which can be solid (for ≤ or ≥) or dashed (for < or >) depending on whether the points on the line are included in the solution set. After graphing the line, you then determine which side of the line represents the solution set by testing a point (usually the origin if it's not on the line) to see if it satisfies the original inequality. Finally, shade the appropriate region to indicate the solutions to the inequality.
How do graph inequalities on a grid?
Graphing inequalities on a grid involves first translating the inequality into an equation to determine the boundary line. For example, for the inequality (y < 2x + 3), you would graph the line (y = 2x + 3) as a dashed line (indicating that points on the line are not included). Next, you select a test point (usually the origin, if it’s not on the line) to determine which side of the line to shade. The shaded region represents all the solutions to the inequality.
What inequality represents the graph?
To determine the inequality that represents a graph, you need to analyze its features, such as the shaded region and the boundary line. If the boundary line is solid, the inequality includes "≤" or "≥," while a dashed line indicates "<" or ">". The shaded region shows where the values satisfy the inequality. By identifying the slope and y-intercept of the line, you can formulate the correct inequality.
How do you describe the steps for graphing a two variable linear inequality?
To graph a two-variable linear inequality, first convert the inequality into an equation by replacing the inequality sign with an equal sign, which gives you the boundary line. Next, graph this line using a solid line for ≤ or ≥ and a dashed line for < or >. Then, determine which side of the line to shade by testing a point not on the line (usually the origin) to see if it satisfies the inequality. Finally, shade the appropriate region to represent all the solutions to the inequality.
When to use a solid line as a boundary when graphing a linear inequality?
If it is <= or >=
What is the region of a coordinate plane that is described by a linear inequality?
The region of a coordinate plane described by a linear inequality consists of all the points that satisfy the inequality, which can be either above or below the boundary line defined by the corresponding linear equation. The boundary line itself is typically dashed if the inequality is strict (e.g., > or <) and solid if it is inclusive (e.g., ≥ or ≤). This region can be unbounded and may extend infinitely in one or more directions, depending on the specific inequality. The solution set includes all points (x, y) that make the inequality true.
Ask us graphing a linear inequality the first step is to replace the inequality symbol with a(n) sign.?
When graphing a linear inequality, the first step is to replace the inequality symbol with an equal sign to graph the corresponding linear equation. This creates a boundary line, which can be solid (for ≤ or ≥) or dashed (for < or >) depending on whether the points on the line are included in the solution set. After graphing the line, you then determine which side of the line represents the solution set by testing a point (usually the origin if it's not on the line) to see if it satisfies the original inequality. Finally, shade the appropriate region to indicate the solutions to the inequality.
How do graph inequalities on a grid?
Graphing inequalities on a grid involves first translating the inequality into an equation to determine the boundary line. For example, for the inequality (y < 2x + 3), you would graph the line (y = 2x + 3) as a dashed line (indicating that points on the line are not included). Next, you select a test point (usually the origin, if it’s not on the line) to determine which side of the line to shade. The shaded region represents all the solutions to the inequality.
How do you know weather to shade above or below the line when graphing an inequality on the coordinate plane?
If the inequality has a > or ≥ sign, you shade above the line. If the inequality has a < or ≤ sign, you shade below it. Obviously, just an = is an equation, not an inequality.
What graph of linear is inequality 6x 2y -10?
The inequality (6x + 2y - 10 > 0) can be rewritten in slope-intercept form as (y > -3x + 5). The boundary line is (y = -3x + 5), which has a slope of -3 and a y-intercept of 5. The region above this line represents the solution set for the inequality. Since the inequality is strict (>), the boundary line itself is not included in the solution.
When will the graph of an equation inequality be a dotted line?
The line is dotted when the inequality is a strict inequality, ie it is either "less than" (<) or "greater than" (>). If there is an equality in the inequality, ie "less than or equal to" (≤), "greater than or equal to" (≥) or "equal to" (=) then the line is drawn as a solid line.
How does the solution to an inequality differ from the solution to an equation?
The solution to an inequality generally is a region with one more dimension. If the inequality/equation is of the form x < a or x = a then the solution to the inequality is the 1 dimensional line segment while the solution to the equality is a point which has no dimensions. If the inequality/equation is in 2 dimensions, the solution to the inequality is an area whereas the solution to the equality is a 1-d line or curve. And so on, in higher dimensional spaces.
How do solutions differ for an equation and an inequality both algebraically and graphically?
Algebraically, solutions to an equation yield specific values that satisfy the equality, while solutions to an inequality provide a range of values that satisfy the condition (e.g., greater than or less than). Graphically, an equation is represented by a distinct curve or line where points satisfy the equality, whereas an inequality is represented by a shaded region that indicates all points satisfying the inequality, often including a boundary line that can be either solid (for ≤ or ≥) or dashed (for < or >). This distinction highlights the difference in the nature of solutions: precise for equations and broad for inequalities.
When graphing inequalities which inequality line is solid?
The line that includes whatever variables are included in the equation.
