Algebra I Lesson 10
Number Relations (Grades 912)
Instruction 104 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 yaxis. To graph such lines, simply find the point x =
m on xaxis and draw the line through this point parallel to yaxis.
Figure 10.10
Horizontal lines have the equations in the form y = n. To draw such equations, simply find a point on yaxis whose coordinate is n. Then, draw a line through this point parallel to the xaxis.
For example, to draw the graph of y = –4, locate point –4 on the yaxis. Then, draw a line through this point that is parallel to xaxis (Figure 10.11).
Figure 10.11
Practical Exercise 3 Draw the graph of the equation 3y = 2 – x.
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