How do you graph inequalities with 2 variables?
The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality. The boundary line is dashed for > and < and solid for ≤ and ≥.
What are the 4 steps in graphing inequalities in 2 two variables?
- Step 1: Solve the inequality for y.
- Step 2: Graph the boundary line for the inequality.
- Step 3: Shade the region that satisfies the inequality.
- Step 4: Solve the second inequality for y.
- Step 5: Graph the boundary line for the second inequality.
- Step 6: Shade the region that satisfies the second inequality.
How do you graph two variables?
Graph a linear equation using the intercepts.
- Find the x– and y-intercepts of the line. Let. and solve for x. Let. and solve for y.
- Find a third solution to the equation.
- Plot the three points and check that they line up.
- Draw the line.
What are two variable inequalities?
A linear inequality in two variables is formed when symbols other than equal to, such as greater than or less than are used to relate two expressions, and two variables are involved. Here are some examples of linear inequalities in two variables: 2x<3y+27x−2y>83x+4y+3≤2y−5y+x≥0.
What is the first step in graphing a linear inequality in two variables?
Steps to Graphing Inequalities:
- Step 1 Change the inequality symbol to “=”. Graph the equation.
- Step 2 Test a point that is not on the line to check whether it is a solution of the inequality.
- Step 3 If the test point is a solution, shade its region. If the test point is not a solution, shade the other region.
How to graph linear inequalities with two variables?
Linear inequalities with two variables have infinitely many ordered pair solutions, which can be graphed by shading in the appropriate half of a rectangular coordinate plane. To graph the solution set of an inequality with two variables, first graph the boundary with a dashed or solid line depending on the inequality.
How to graph the inequality 2y > 4x-6?
Graph the inequality 2y > 4x–6 2 y > 4 x – 6. Solve for y. Create a table of values to find two points on the line y = 2 x − 3 y = 2 x − 3. Plot the points and graph the line. The line is dotted because the sign in the inequality is >, not ≥ and therefore points on the line are not solutions to the inequality.
When to use dotted line or solid line to graph inequality?
If points on the boundary line are solutions, then use a solid line for drawing the boundary line. This will happen for ≤ or ≥ inequalities. If points on the boundary line are not solutions, then use a dotted line for the boundary line. This will happen for < or > inequalities.
How to find the slope of an inequality?
Step 1: Graph the boundary. Because of the strict inequality, we will graph the boundary y = − 3x + 1 using a dashed line. We can see that the slope is m = − 3 = − 3 1 = rise run and the y -intercept is (0, 1).