136 Part 2: Into the Unknown
CHECK POINT
Plot each point in the coordinate plane.- (1,8)
- (-6,2)
- (3,-6)
4. (-4,-1)
5. (0,2)
Graphing Linear Equations
Our coordinate system assigns a pair of numbers to every point and a point to every pair of
numbers. The power of such a system is that it lets you give a picture of all the pairs of numbers
that solve an equation or inequality with two variables.Graphs as Pictures of Patterns
The graph of an equation in two variables is a picture of all the pairs of numbers that balance the
equation. An equation in two variables has infinitely many solutions, each of which is an ordered
pair (x,y). The graph of the equation is a picture of all the possible solutions. Because each of
those pairs of numbers fits the same rule, when you plot the points, you find that they fall in a
pattern, specifically a line. That’s why these equations are sometimes called linear equations.Plotting Points
The most straightforward way to graph an equation is to choose several values for x, substitute
each value into the equation, and calculate the corresponding values for y. This information can
be organized into a table of values. Two points are technically enough to determine a line, but
when building a table of values, it is wise to include several more, so that any errors in arithmetic
will stand out as deviations from the pattern.