how do you graph linear inequlities in two variable
To graph linear inequalities in two variables, such as "y > mx + b" or "ax + by > c," you can follow these steps:
Step 1: Rewrite the inequality in slope-intercept form (y = mx + b) if it's not already in that form. For example, if you have "2x - 3y > 6," rewrite it as "-3y > -2x + 6" and then divide everything by -3 to get "y < (2/3)x - 2."
Step 2: Draw the graph of the related equation, but use a dashed line instead of a solid line. For example, if the related equation is "y = (2/3)x - 2," draw a dashed line with a slope of 2/3 and a y-intercept of -2.
Step 3: Determine whether to shade the region above or below the line. Test a point that is not on the line. If the inequality is true for that point, shade the region containing that point; otherwise, shade the opposite region.
Step 4: Graph the shaded region by using arrows or shading. If the inequality is "less than" or "greater than," use dashed arrows pointing towards the shaded region. If the inequality is "less than or equal to" or "greater than or equal to," use solid arrows pointing towards the shaded region.
Step 5: Make sure to label the x-axis and y-axis, and add any additional information, such as the inequalities or equations.
Remember, it's always a good idea to choose a few test points (one in each shaded region) to verify that the graph is accurate.