graphing inequalities on a coordinate plane

Starting from the origin, go along the x-axis in a positive direction (right) and along the y-axis in a negative direction (down). Starting from the origin, go along the x-axis in a negative direction (left) and along the y-axis in a negative direction (down). Starting from the origin, go along the x-axis in a negative direction (left) and along the y-axis in a positive direction (up). Starting from the origin, go along the x-axis in a positive direction (right) and along the y-axis in a positive direction (up).

They also follow a pattern, which is outlined in the table below. Within each quadrant, the signs of the x-coordinates and y-coordinates of each ordered pair are the same. What do you notice about the signs of the x- and y-coordinates of the points within each quadrant? Look at each quadrant in the graph below. Ordered pairs within any particular quadrant share certain characteristics. Quadrants are named using the Roman numerals I, II, III, and IV beginning with the top right quadrant and moving counter clockwise.

These four sections are called quadrants. The intersecting x- and y-axes of the coordinate plane divide it into four sections. Identify quadrants and use them to plot points If the y-coordinate is positive, move up if the y-coordinate is negative, move down. Beginning at the x-coordinate, move vertically, the direction of the y-axis, the distance given by the y-coordinate. If the x-coordinate is positive, move to the right if the x-coordinate is negative, move to the left. Beginning at the origin, move horizontally, the direction of the x-axis, the distance given by the x-coordinate. The line is solid because ≤ means “less than or equal to,” so all ordered pairs along the line are included in the solution set.Steps for Plotting an Ordered Pair ( x, y) in the Coordinate Plane Plot the points (0,1) and (4,0), and draw a line through these two points for the boundary line. You can use the x– and y-intercepts for this equation by substituting 0 in for x first and finding the value of y then substitute 0 in for y and find x. To graph the boundary line, find at least two values that lie on the line x+4y=4.

If points on the boundary line aren’t solutions, then use a dotted line for the boundary line.

This will happen for ≤ or ≥ inequalities.

If points on the boundary line are solutions, then use a solid line for drawing the boundary line.

Shade the region that contains the ordered pairs that make the inequality a true statement.

Identify at least one ordered pair on either side of the boundary line and substitute those (x,y) values into the inequality.

Replace the, ≤ or ≥ sign in the inequality with = to find the equation of the boundary line. A false statement means that the ordered pair is not a solution, and the point will graph outside the shaded region, or the point will be part of a dotted boundary line. If substituting (x,y) into the inequality yields a true statement, then the ordered pair is a solution to the inequality, and the point will be plotted within the shaded region or the point will be part of a solid boundary line. Here is an example from the section on solving linear inequalities: An ordered pair is used to locate points on the coordinate plane. (The numbering starts in the top right quadrant and goes counter-clockwise). The quadrants are numbered with roman numerals. Recall that solutions to linear inequalities typically lead to an infinite number of solutions represented by an interval of values. The axes split the coordinate plane into 4 quadrants. Identify the difference between the graph of a linear equation and linear inequality

Graph a linear inequality in two variables.

Graph horizontal and vertical inequalities.

A boundary line, which is the related linear equation, serves as the boundary for the region.You can use a visual representation to figure out what values make the inequality trueand also which ones make it false.

Determine if an ordered pair satisfies a linear inequality Linear inequalities can be graphed on a coordinate plane.The solutions for a linear inequality are in a region of the coordinate plane.

Graphing inequalities on a coordinate plane