graph the inequality in the coordinate plane

By the end of this guide, you will be able to: A : ( 0, − 3 ) y = 2 x − 3 − 3 = ? 2 ( 0 ) − 3 − 3 = − 3 ✓ ( 0, − 3 ) is a solution.Welcome to this simple and straightforward guide to graphing linear inequalities on the coordinate plane. Substitute the x x- and y y-values into the equation to check if the ordered pair is a solution to the equation.Ī : ( 0, − 3 ) y = 2 x − 3 − 3 = ? 2 ( 0 ) − 3 − 3 = − 3 ✓ ( 0, − 3 ) is a solution. Every solution of this equation is a point on this line.įigure 5.25 Graph of y = 2 x – 3 y = 2 x – 3.Every point on the line is a solution of the equation.Points not on the line are not solutions! The graph of a linear equation A x + B y = C A x + B y = C is a straight line. This line is called the graph of the equation. And every solution of the linear equation is on this line. Every point on the line is a solution of that linear equation.

The line shows you all the solutions to that linear equation. We put arrows on the ends of each side of the line to indicate that the line continues in both directions.Ī graph is a visual representation of all the solutions of a linear equation. We connect the points with a straight line to get the graph of the linear equation. The points will line up perfectly in a straight line. We can plot these solutions in the rectangular coordinate system. When we substitute these values of x x and y y into the equation, the result is a true statement, because the value on the left side is equal to the value on the right side. This pair of values is a solution to the linear equation and is represented by the ordered pair ( x x, y y). For every number that is substituted for x x there is a corresponding y y value. Linear equations have infinitely many solutions. Most people prefer to have A A, B B, and C C be integers and A ≥ 0 A ≥ 0 when writing a linear equation in standard form, although it is not strictly necessary.

When an equation is in the form A x + B y = C A x + B y = C, we say it is in standard form of a linear equation. 3 x + y = 5 3 x + y = 5īy rewriting y = − 3 x + 5 y = − 3 x + 5 as 3 x + y = 5 3 x + y = 5, we can easily see that it is a linear equation in two variables because it is of the form A x + B y = C A x + B y = C. Step 3: Put it in A x + B y = C A x + B y = C form. We can use the addition property of equality and rewrite it in A x + B y = C A x + B y = C form. But it does not appear to be in the form A x + B y = C A x + B y = C. The equation y = − 3 x + 5 y = − 3 x + 5 is also a linear equation. Here is an example of a linear equation in two variables, x x and y y.Ī x + B y = C A + 4 y = 8 A = 1, B = 4, C = 8 A x + B y = C A + 4 y = 8 A = 1, B = 4, C = 8 An equation of this form, where A A and B B are both not zero, is called a linear equation in two variables. Equations with two variables may be of the form A x + B y = C A x + B y = C. But equations can have more than one variable. In almost every case, when you solved the equation, you got exactly one solution. Up to now, all the equations you have solved were equations with just one variable. Graphing Linear Equations in Two Variables The point ( 3, 5 2 ) ( 3, 5 2 ) is in quadrant I. Since y = 5 2 y = 5 2, which is equal to 2.5, the point is above the x x-axis. Since x = 3 x = 3, the point is to the right of the y y-axis.Since x = 0 x = 0, the point whose coordinates are ( 0, − 1 ) ( 0, − 1 ) is on the y y-axis.The point ( 2, − 3 ) ( 2, − 3 ) is in quadrant IV. Since y = − 3 y = − 3, the point is below the x x-axis. Since x = 2 x = 2, the point is to the right of the y y-axis.The point ( − 3, − 4 ) ( − 3, − 4 ) is in quadrant III. Also, since y = − 4 y = − 4, the point is below the x x-axis. Since x = − 3 x = − 3, the point is to the left of the y y-axis.The point ( − 5, 4 ) ( − 5, 4 ) is in quadrant II. Also, since y = 4 y = 4, the point is above the x x-axis. Since x = − 5 x = − 5, the point is to the left of the y y-axis.

The first number of the coordinate pair is the xFigure 5.24). Plot the following points in the rectangular coordinate system and identify the quadrant in which the point is located:

Graph the inequality in the coordinate plane