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Exercises Equations and inequalities

Example 2 from Algebra and Trigonometry, 2.1 The Rectangular Coordinate Systems and Graphs

Graphing an Equation in Two Variables by Plotting Points

Graph the equation $y = - x + 2$ by plotting points.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

1

Solution

First, we construct a table similar to Table 2. Choose x values and calculate y.

$x$	$y = - x + 2$	$(x, y)$
$−5$	$y = - (−5) + 2 = 7$	$(−5, 7)$
$−3$	$y = - (−3) + 2 = 5$	$(−3, 5)$
$−1$	$y = - (−1) + 2 = 3$	$(1, 1)$
$3$	$y = - (3) + 2 = −1$	$(3, −1)$
$5$	$y = - (5) + 2 = −3$	$(5, −3)$
$3$	$y = - (3) + 2 = −1$	$(3, −1)$
$5$	$y = - (5) + 2 = −3$	$(5, −3)$

Table 2

Now, plot the points. Connect them if they form a line. See Figure 7

This image is a graph of a line on an x, y coordinate plane. The x-axis includes numbers that range from negative 7 to 7. The y-axis includes numbers that range from negative 5 to 8. A line passes through the points: (-5, 7); (-3, 5); (-1, 3); (0, 2); (1, 1); (3, -1); and (5, -3).

Figure 7

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Construct a table and graph the equation by plotting points: $y = \frac{1}{2} x + 2.$

How did it go?

PreviousPlotting Points in a Rectangular Coordinate System Next Using a Graphing Utility to Graph an Equation

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 2.1, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.