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Chapter 12—Graphing

12-2 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 P1 = (4, 5) and P2 = (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 lead-in 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 y-coordinate is always 2, no matter what the x-coordinate might be. The ordered pair for this particular horizontal line  is (x,2)

Looking at the vertical line, you can see that the x-coordinate is always 4,  no matter what the y-coordinate might be. An  ordered-pair  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 y-axes. The point where the line crosses the x-axis is the x-intercept. The point where the line crosses the y-axis is the y-intercept.   The y-intercept occurs where the line crosses the y-axis, so it is shown as the ordered pair (0,y). The x-coordinate is always zero where the line crosses the y-axis. The x-intercept occurs where the line crosses the x-axis, so it is shown as the ordered pair (x,0). The y-coordinate is always zero where the line crosses the x-axis. 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 x-axis. This will be the x-intercept for the line. You can see that point is at (8,0). So the x-intercept for this line is shown as (8,0) Step 2: Find the point where the line crosses the y-axis. This will be the y-intercept for the line. You can see that point is at (0,4). So the y-intercept for this line is shown as (0,4)   Note: It makes no difference which intercept you find first.

Example

 Problem:  Determine the x- and y-intercepts for this line. Step 1: Find the coordinate where the line crosses the x-axis Step 2: Find the coordinate where the line crosses the y-axis Solution: x-intercept = (4,0) y-intercept = (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 y-intercepts 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 y-intercepts are sufficient for defining a straight line.[

Example

Exercises

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