Chapter 21

Graphing Basics

Graphing in algebra amounts to plotting points and, often, connecting them. The points are placed by using the Cartesian coordinates, so named for Rene Descartes, a prolific mathematician who dabbled in many areas and made many contributions. The points are assigned their positions by distances from a central point, called the origin. The ordered pairs that name points, (x, y), always have the horizontal movement listed first and the vertical movement listed second.

The Problems You'll Work On

In this chapter, you'll graph and plot and work with Cartesian coordinates in the following ways:

  • Plotting points correctly on the coordinate plane
  • Recognizing point positions in terms of their quadrant or position on an axis
  • Finding the intersection of two lines
  • Computing slopes from points or determining slopes from equations of lines
  • Graphing lines by using points and slopes
  • Graphing lines by using more than one point

What to Watch Out For

The following points are important to keep in mind as you work through this chapter:

  • Plotting points on the correct axis; (0, y) is on the y-axis and (x, 0) is on the x-axis.
  • Using the slope formula correctly by keeping the order of the coordinates the same
  • Remembering that slope is change-in-y divided by change-in-x
  • Counting off slope correctly when graphing lines

Plotting Points on the Coordinate System

886−889 Identify the graphed point.

886. Which is the graph of (−2, 3)?

image

887. Which is the graph of (4, −1)?

image

888. Which is the graph of (0, 2)?

image

889. Which is the graph of (−4, 0)?

image

Determining the Quadrant of a Point

890−893 Name the quadrant or axis where you find the point.

890.

image

891.

image

892.

image

893.

image

Finding the Intercepts of a Line

894−903 Find the intercepts of the lines.

894. 3x + 2y = 6

895. 4x − 3y = 12

896. 5x + 2y = 0

897. 6x − y = 0

898. y = 4x − 3

899. y = −x + 2

900. image

901. image

902. y = 8

903. x = −3

Calculating the slope of a line from two points

904−909 Find the slope of the line through the two given points.

904. (2, 3) and (−1, 6)

905. (0, 4) and (5, −9)

906. (−4, −3) and (5, −2)

907. (0, 5) and (−4, 0)

908. (6, 5) and (−3, 5)

909. (−4, 2) and (−4, −4)

Determining a Line's Slope from Its Equation

910−915 Find the slope of the line given its equation.

910. y = −4x + 3

911. y = 2x − 1

912. 3x + 6y = 11

913. 4x − 3y = 7

914. y = −6

915. x = 3

Sketching the Graph of a Line from Its Equation

916−921 Sketch a graph of the line using the slope-intercept form, and determine a point that the line passes through.

916. y = 3x − 1

917. y = −2x + 3

918. image

919. image

920. y = 2

921. y = −4

Sketching Lines Using Two Points

922−925 Sketch the graph of a line using the two points.

922. (−2, 2) and (1, −3)

923. (3, 0) and (−1, −1)

924. (−2, 3) and (5, 3)

925. (0, −2) and (−4, 0)

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