Algebra I Lesson 10
Number Relations (Grades 9-12)

 Instruction 10-4 Ordered Pairs |Relations | Equations as Relations | Graphing Linear Relations | Summary GRAPHING LINEAR RELATIONS   CACS Algebra 16.0 & 17.0 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.   Links for Students, Parents and Teachers Now let's do Practice Exercise 10-4 (top) Choose printer friendly or online exercises. Printer friendly version requires the Adobe Acrobat Reader 5. Click HERE to obtain a free copy.     Next Page:  Problems (top)