I need to graph solution sets for linear inequalities. How do I do this?
I've done these kind already send me an example of one and i'll explain its probably similar to the ones i did.
To graph solution sets for linear inequalities, you can follow these steps:
1. Start by writing the equation of the inequality in slope-intercept form: y = mx + b. Here, m represents the slope, and b represents the y-intercept.
2. Graph the inequality as if it were an equation with an equal sign. To do this, plot the y-intercept (b) on the y-axis.
3. Use the slope (m) to determine additional points on the graph. To find these points, you can either use the rise-over-run method or the slope-intercept form of a line. If the slope is a whole number, the rise-over-run method is convenient. For example, if the slope is 2/3, start at the y-intercept and move 2 units up and 3 units to the right. Connect these points to create a line.
4. Determine whether the inequality is a "less than" or "greater than" inequality. If it is a "less than" inequality (represented by < or ≤), the line you just drew should be a dashed line. If it is a "greater than" inequality (represented by > or ≥), the line should be solid.
5. Choose a point not on the line. You can pick any point in the coordinate plane but avoiding points on the line makes it easier. Test this point by substituting its x- and y-values into the original inequality. If the inequality is true, shade the side of the line containing that point. If it is false, shade the other side.
By following these steps, you can accurately graph the solution set for linear inequalities.
Regarding an example, here is a linear inequality: y < 2x + 1. To graph this inequality, you would start by graphing the line y = 2x + 1 as a dashed line since it is a "less than" inequality. Then, you would pick a point (not on the line) such as (0,0) and substitute its values into the inequality: 0 < 2(0) + 1. Since this is true, you would shade the side of the line containing the point (0,0).