How do you graph linear inequalities step by step?

How do you graph linear inequalities step by step?

1. Step 1: Solve the inequality for y.
2. Step 2: Graph the boundary line for the inequality.
3. Step 3: Shade the region that satisfies the inequality.
4. Step 4: Solve the second inequality for y.
5. Step 5: Graph the boundary line for the second inequality.
6. Step 6: Shade the region that satisfies the second inequality.

How do you solve a linear inequality and graph it?

There are three steps:

1. Rearrange the equation so “y” is on the left and everything else on the right.
2. Plot the “y=” line (make it a solid line for y≤ or y≥, and a dashed line for y< or y>)
3. Shade above the line for a “greater than” (y> or y≥) or below the line for a “less than” (y< or y≤).

What is the graph of a linear inequality?

To graph a linear inequality in two variables (say, x and y ), first get y alone on one side. The graph of this equation is a line. If the inequality is strict ( < or > ), graph a dashed line. If the inequality is not strict ( ≤ or ≥ ), graph a solid line.

What is the graph of linear inequality?

How do you graph two linear inequalities?

To graph a linear inequality in two variables (say, x and y ), first get y alone on one side. Then consider the related equation obtained by changing the inequality sign to an equality sign. The graph of this equation is a line. If the inequality is strict ( < or > ), graph a dashed line.

How do you find a linear inequality?

Unless you are graphing a vertical line the sign of the inequality will let you know which half-plane to shade. If the symbol ≥ or > is used, shade above the line. If the symbol ≤ or < is used shade below the line. For a vertical line, larger solutions are to the right and smaller solutions are to the left.

How do you graph a linear equation?

To graph an equation using the slope and y-intercept, 1) Write the equation in the form y = mx + b to find the slope m and the y-intercept (0, b). 2) Next, plot the y-intercept. 3) From the y-intercept, move up or down and left or right, depending on whether the slope is positive or negative.

How do you graph linear inequalities in math?

Graphing Linear Inequalities. This is a graph of a linear inequality: The inequality y ≤ x + 2. You can see the y = x + 2 line, and the shaded area is where y is less than or equal to x + 2. A Linear Inequality is like a Linear Equation (such as y = 2x+1) … but it will have an Inequality like <, >, ≤, or ≥ instead of an =.

How do you find the solution set of an inequality?

1 Replace the inequality symbol with an equal sign and graph the resulting line. 2 Check one point that is obviously in a particular half-plane of that line to see if it is in the solution set of the inequality. 3 If the point chosen is in the solution set, then that entire half-plane is the solution set.

How to solve a system of two linear equations by graphing?

To solve a system of two linear equations by graphing, graph the equations carefully on the same coordinate system. Their point of intersection will be the solution of the system. To solve a system of two linear inequalities by graphing, determine the region of the plane that satisfies both inequality statements.

How do you find the x-intercept of a linear inequality?

Alternatively, we can determine the x-intercept and the y-intercept of the standard form linear inequality by subtituting y = 0, then solve for x and substituting x = 0, then solve for y respectively. Recall that the x-intercept is the value of x when y = 0 and the y-intercept is the value of y when x = 0.