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Chapter 12—Graphing 122 Plotting Lines on the Coordinate Plane
Topics Covered in this Lesson  Introduction to points and lines on the coordinate plane
 Plotting lines through pairs of points on the coordinate plane
 Two Special Lines: Horizontal and Vertical
 Introduction to Intercepts
 Determining the Intercepts of a Line
 Plotting a Line, Given Its Intercepts
 Points plotted on a coordinate plane.  Lines plotted on a coordinate plane.  If you can plot points on a coordinate plane, you can also plot lines. In fact, you can plot all sorts of points, lines, planes and graphs on a coordinate plane. But let's not get ahead of ourselves, and focus on the idea of plotting straight lines on the coordinate plane.  If you can plot two points, you can plot a straight line.
 Simply plot the two points and draw a straight line between them.
You can't define a line from just one point. Think about it. If you have just one point on the coordinate plane, you can plot an endless number of different lines through it — up, down, sideways, at all sorts of angle .... But!! But if you plot two points, you can define one particular line. No others. Two lines. Notice how each one is drawn between two points.  Plotting Lines Through Pairs Of Points Example Problem: Plot a straight line between points P_{1} = (4, 5) and P_{2} = (1, 1). Step 1: Plot the first point.  Step 2: Plot the second point.  Step 2: Draw a straight line between the two points.  More Examples Exercises Work on these endless examples and exercises until you can plot coordinates of points on a plane ... without error. Locating Points on a Line Given a line on a coordinate place, cite the coordinates for a least two points on the line. Endless Examples & Exercises [note: this is a leadin to graphing linear equations y = f(x) Two Special Lines: Horizontal and Vertical Definitions  A horizontal line is a straight line that lies parallel to the x axis on the coordinate plane. If the coordinate plane is set up in the customary fashion, horizontal lines on the plane run straight left and right.
 A vertical line is a straight line that lies parallel to the y axis on the coordinate plan. If the coordinate plane is set up in the customary fashion, vertical lines on the plane run straight up and down.
   Looking at the horizontal line that is plotted on the graph above, you can see that the ycoordinate is always 2, no matter what the xcoordinate might be. The ordered pair for this particular horizontal line is (x,2) Looking at the vertical line, you can see that the xcoordinate is always 4, no matter what the ycoordinate might be. An orderedpair expression for this line would be (4,y) Examples Exercise Use this exercises to master your recognition of horizontal and vertical lines based only upon a pair of points on that line. You might need to sketch the line for the first few exercises. But you should work on creating a mental image of the line and answer the prompts very quickly. Introduction to Intercepts Definition  The intercepts of a line are the two special points where the line crosses the x and yaxes.  The point where the line crosses the xaxis is the xintercept.
 The point where the line crosses the yaxis is the yintercept.
The yintercept occurs where the line crosses the yaxis, so it is shown as the ordered pair (0,y). The xcoordinate is always zero where the line crosses the yaxis. The xintercept occurs where the line crosses the xaxis, so it is shown as the ordered pair (x,0). The ycoordinate is always zero where the line crosses the xaxis.   Determine the Intercepts of a Line Procedure  When you are shown a straight line on a coordinate plane, you can easily locate the intercepts by inspection. Step 1: Find the point where the line crosses the xaxis. This will be the xintercept for the line. You can see that point is at (8,0). So the xintercept for this line is shown as (8,0) Step 2: Find the point where the line crosses the yaxis. This will be the yintercept for the line. You can see that point is at (0,4). So the yintercept for this line is shown as (0,4) Note: It makes no difference which intercept you find first.   Example Problem: Determine the x and yintercepts for this line.  Step 1: Find the coordinate where the line crosses the xaxis  Step 2: Find the coordinate where the line crosses the yaxis     Solution:  xintercept = (4,0)
 yintercept = (0,2)
  More Examples Exercises Plot a Line, Given Its Intercepts You have already learned how to plot a straight line between two different points on a coordinate plane. The x and yintercepts for a line are simply two points of special significance  they lay directly on their respective axes. But the are nevertheless two point on the coordinate plane, and a pair of coordinates for the x and yintercepts are sufficient for defining a straight line.[ Example Exercises
