Instruction 10-4

Ordered Pairs |Relations | Equations as Relations | Graphing Linear Relations | Summary

Graphing any linear equation is a simple task. You need to have at least two ordered pairs of the equation. Locating these pairs in a coordinate plane and passing a line through these points gives the graph of the equation.

Let try to graph an equation y = –x + 5. Find two ordered pairs of the equation. Let take two arbitrary point x = 2 and x = 3. Find the corresponding y’s of these x’s.

(a)               x = –2  y = –2 + 5

    = 3

(b)               x = –3  y = –3 + 5

                               = 2

Now, we have two ordered pairs of the given equation: (2, 3) and (3, 2). Locate these pairs in a coordinate plane and pass a line through them (Figure 10.7).

Figure 10.7

Practice 8

Determine which pairs of points can be used for drawing each equation.

Equations                                                        

y = 3x – 5

y = –2x – 4

y = 3x – 6

y = –x – 1

Ordered Pairs

(8, –20), (2, –3), (2, 0), (1, –2), (–4, 4), (6, 13), (–2, 1), (0, –6)

Answers

Practice 9

Graph equation y = 3x – 6.

Solution

Find two ordered pairs that satisfy the given equation. Choose two arbitrary values x = 1 and x = 2. Find the corresponding values of y.

x = 1  y = 3(1) – 6

                                           = 3 – 6

                                         = –3

x = 2   y = 3(2) – 6

                     = 6 – 6

                        = 0

Now, locate points (1, –3) and (2, 0) in a coordinate plane and draw a line through these points (Figure 10.9). Remember the arrows on each end of the line.

Figure 10.9

 Graphing a Vertical Line

Lines that have equations of the form x = m are graphed vertically or parallel to the y-axis. To graph such lines, simply find the point x = m on x-axis and draw the line through this point parallel to y-axis.

For example in order to draw the graph of x = –3, simply find the point x = –3 on x-axis. Then draw a line through this point parallel to y-axis (Figure 10.10).

Figure 10.10

Graphing a Horizontal Line

 Horizontal lines have the equations in the form y = n. To draw such equations, simply find a point on y-axis whose coordinate is n. Then, draw a line through this point parallel to the x-axis.

For example, to draw the graph of y = –4, locate point –4 on the y-axis. Then, draw a line through this point that is parallel to x-axis (Figure 10.11).

Figure 10.11

Practical Exercise 3

Draw the graph of the equation 3y = 2 – x.

Answer

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