These solutions, when plotted, give a curved line (nonlinear). Notice that these solutions, when plotted, do not form a straight line. Now plot these coordinates as shown in Figure 6. The line that passes through the points graphed in Figure 4.Įquations that have a variable raised to a power, show division by a variable, involve variables with square roots, or have variables multiplied together will not form a straight line when their solutions are graphed. Complete the graph of x + y = 6 by drawing the line that passes through these points (see Figure 5).įigure 5. Equations whose solution sets form a straight line are called linear equations. Notice that these solutions, when plotted, form a straight line. Now plot these coordinates as shown in Figure 4.įigure 4. (When giving a value for one variable, you could start with 0, then try 1, and so on.) Then graph the solutions. Repeat this process to find other coordinates. To graph an equation on the coordinate plane, find the coordinate by giving a value to one variable and solving the resulting equation for the other value. Graphing equations on the coordinate plane In quadrant IV, x is always positive and y is always negative.In quadrant III, x and y are both always negative.In quadrant II, x is always negative and y is always positive.In quadrant I, x is always positive and y is always positive.These quadrants are labeled in Figure 3.įigure 3. The coordinate graph is divided into four quarters called quadrants. The x‐coordinate shows the right or left direction, and the y‐coordinate shows the up or down direction. Also, note that the first number in the ordered pair is called the x ‐coordinate, or abscissa, and the second number is the y ‐coordinate, or ordinate. On the y‐axis, numbers above 0 are positive and below 0 are negative. Notice that on the x‐axis numbers to the right of 0 are positive and to the left of 0 are negative. Some coordinates are noted in Figure 2.įigure 2. The point of intersection of the two number lines is called the origin and is represented by the coordinates (0, 0).Įach point on a plane is located by a unique ordered pair of numbers called the coordinates. The other is vertical and is called the y ‐axis. One axis is horizontal and is called the x ‐axis. In coordinate graphs (see Figure 1), two perpendicular number lines are used and are called coordinate axes. These numbers represent the placement of the point relative to two intersecting lines. In the same way, each point in a plane is assigned a pair of numbers. Each point on a number line is assigned a number. Quiz: Linear Inequalities and Half-PlanesĬoordinate geometry deals with graphing (or plotting) and analyzing points, lines, and areas on the coordinate plane (coordinate graph).Solving Equations Containing Absolute Value. Inequalities Graphing and Absolute Value.Quiz: Operations with Algebraic Fractions.Quiz: Solving Systems of Equations (Simultaneous Equations).Solving Systems of Equations (Simultaneous Equations).Quiz: Variables and Algebraic Expressions.Quiz: Simplifying Fractions and Complex Fractions.Simplifying Fractions and Complex Fractions.Quiz: Signed Numbers (Positive Numbers and Negative Numbers).Signed Numbers (Positive Numbers and Negative Numbers).Quiz: Multiplying and Dividing Using Zero.Quiz: Properties of Basic Mathematical Operations.
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