how to graph an inequality step by step
To graph an inequality step by step, follow these steps:
1. Start by rewriting the inequality, if necessary, in slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.
(Example: If you have an inequality like 2x + 3y ≤ 6, rewrite it as y ≤ -2/3x + 2).
2. Draw the graph of the equation that corresponds to the equality part of the inequality. You can treat it as an equation of a line and graph it accordingly. Use a solid line if the inequality includes "or equal to" (≤ or ≥) and a dashed line if the inequality is strictly less than or greater than (< or >).
3. Select a test point not on the line. Ideally, choose the origin (0,0), but any other point will work as well.
4. Substitute the x and y coordinates of the test point into the original inequality.
- If the inequality is true, shade the region of the test point.
- If the inequality is false, shade the opposite region.
5. Graphically represent the shaded region. If the inequality is "less than" or "greater than," shade the region on the side of the line away from the test point, known as the "unbounded side." If the inequality is "less than or equal to" or "greater than or equal to," shade the region on the side of the line that includes the test point, known as the "bounded side."
6. Lastly, label the shaded region as the solution to the inequality.
Remember to double-check your graph and ensure it accurately represents the original inequality, especially regarding solid versus dashed lines, and the direction of inequality symbols.
simple pls
Sure! Here is a simplified step-by-step guide to graph an inequality:
1. Start with the inequality given. Make sure it is in the form "y <" or "y >" or "y ≤" or "y ≥" or "y =" with some expression.
2. Treat the corresponding equality (without the inequality symbol) as if it were an equation and graph it. If it's already in the form "y = mx + b", then the graph will be a straight line.
3. If the inequality symbol is "<" or ">", draw a dashed line to represent it. If the symbol is "≤" or "≥", draw a solid line to represent it.
4. Choose a test point that is not on the line (e.g., (0,0)).
5. Substitute the test point's x and y values into the original inequality. If it is true, shade the side of the graph containing the test point. If false, shade the opposite side.
6. Finally, label the shaded area as the solution to the inequality.
Remember to check that your graph accurately represents the original inequality, including the direction of the inequality symbol and solid vs. dashed lines.