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.
In this chapter, you'll graph and plot and work with Cartesian coordinates in the following ways:
The following points are important to keep in mind as you work through this chapter:
886−889 Identify the graphed point.
886. Which is the graph of (−2, 3)?
887. Which is the graph of (4, −1)?
888. Which is the graph of (0, 2)?
889. Which is the graph of (−4, 0)?
890−893 Name the quadrant or axis where you find the point.
890.
891.
892.
893.
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.
901.
902. y = 8
903. x = −3
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)
909. (−4, 2) and (−4, −4)
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
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.
919.
920. y = 2
921. y = −4
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)