If the inequality includes 'or equal' then use a solid dot [the value is included]. If it doesn't use 'or equal' then use the open dot.
if you have y <= f(x), then graph the function y = f(x) with a solid line, then shade everything below that graph.
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.
I think you would use an average two step equation to solve. Graph on a number line. If it was -2, go over 2 to the left, and make a dot. It is hollow or solid. It is solid if there is a line beneath the less than or greater than sign indicating that it is equal to....
Vertex
If it is <= or >=
The graph of an inequality is a region, not a line.
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.
To graph an inequality in two variables, first graph the corresponding linear equation as if it were an equality. Use a dashed line if the inequality is strict (e.g., < or >) to indicate that points on the line are not included, or a solid line for non-strict inequalities (e.g., ≤ or ≥). Next, determine which side of the line to shade by selecting a test point not on the line (commonly the origin) and checking if it satisfies the inequality. Shade the region that includes all solutions to the inequality.
To accurately determine which inequality is shown in the graph, I would need to see the graph itself. However, if the graph displays a shaded region above a line, it typically represents a "greater than" inequality (e.g., y > mx + b), while shading below the line indicates a "less than" inequality (e.g., y < mx + b). Additionally, if the line is solid, it indicates that the points on the line are included in the solution (≥ or ≤), whereas a dashed line indicates they are not (>, <).
To write the inequality represented by a graph, first identify the boundary line, which can be solid (indicating '≤' or '≥') or dashed (indicating '<' or '>'). Determine which side of the line is shaded, as this indicates the solution set. Use a test point, often the origin (0,0), to confirm whether it satisfies the inequality. Finally, combine this information to express the inequality in standard form.
FALSE
if you have y <= f(x), then graph the function y = f(x) with a solid line, then shade everything below that graph.
If the points that are ON the line satisfy the inequality then the line should be solid. Otherwise it should be dotted. Another way of putting that is, if the inequality is given in terms of ≤ or ≥, then use a solid line. If they are < or > use 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.
The graph of an inequality in the coordinate plane represents a region that satisfies the inequality. For example, the inequality (y < 2x + 3) would be graphed by first drawing the line (y = 2x + 3) as a dashed line (indicating that points on the line are not included), and then shading the area below the line, which contains all the points that satisfy the inequality. The boundary line can be solid if the inequality is "less than or equal to" or "greater than or equal to."
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.
To determine which graph represents the solution to a system of linear inequalities, you need to identify the boundaries defined by each inequality and their respective regions. Each inequality will create a half-plane, and the feasible solution set is where these half-planes overlap. The graph should show solid lines for inequalities that include equalities (≤ or ≥) and dashed lines for strict inequalities (< or >). Look for the region that satisfies all inequalities simultaneously.