{"id":8618,"date":"2017-05-26T16:42:07","date_gmt":"2017-05-26T16:42:07","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&p=8618"},"modified":"2019-05-27T05:52:41","modified_gmt":"2019-05-27T05:52:41","slug":"use-the-rectangular-coordinate-system","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/chapter\/use-the-rectangular-coordinate-system\/","title":{"raw":"Introduction to Plotting Points on the Rectangular Coordinate System","rendered":"Introduction to Plotting Points on the Rectangular Coordinate System"},"content":{"raw":"

What you'll learn to do: Plot points on the rectangular coordinate system and find solutions to linear equations<\/h2>\r\n

\"This<\/h2>\r\nCyclists speed toward the finish line.Which cyclist will win the race? What will the winning time be? How many seconds will separate the winner from the runner-up? One way to summarize the information from the race is by creating a graph. In this chapter, we will discuss the basic concepts of graphing. The applications of graphing go far beyond races. They are used to present information in almost every field, including healthcare, business, and entertainment.\r\n\r\nBefore you get started in this module, try a few practice problems and review\u00a0prior\u00a0concepts.\r\n
\r\n

Readiness Quiz<\/h3>\r\n1)[ohm_question]144878[\/ohm_question]\r\n\r\nIf you missed this problem, review the example below.\r\n
\r\n\r\nEvaluate [latex]x+7[\/latex] when\r\n
    \r\n \t
  1. [latex]x=3[\/latex]<\/li>\r\n \t
  2. [latex]x=12[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"528374\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"528374\"]\r\n\r\nSolution:\r\n\r\n1. To evaluate, substitute [latex]3[\/latex] for [latex]x[\/latex] in the expression, and then simplify.\r\n\r\n\r\n\r\n\r\n\r\n
    <\/td>\r\n[latex]x+7[\/latex]<\/td>\r\n<\/tr>\r\n
    Substitute.<\/td>\r\n[latex]\\color{red}{3}+7[\/latex]<\/td>\r\n<\/tr>\r\n
    Add.<\/td>\r\n[latex]10[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nWhen [latex]x=3[\/latex], the expression [latex]x+7[\/latex] has a value of [latex]10[\/latex].\r\n2. To evaluate, substitute [latex]12[\/latex] for [latex]x[\/latex] in the expression, and then simplify.\r\n\r\n\r\n\r\n\r\n\r\n
    <\/td>\r\n[latex]x+7[\/latex]<\/td>\r\n<\/tr>\r\n
    Substitute.<\/td>\r\n[latex]\\color{red}{12}+7[\/latex]<\/td>\r\n<\/tr>\r\n
    Add.<\/td>\r\n[latex]19[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nWhen [latex]x=12[\/latex], the expression [latex]x+7[\/latex] has a value of [latex]19[\/latex].\r\n\r\nNotice that we got different results for parts 1 and 2 even though we started with the same expression. This is because the values used for [latex]x[\/latex] were different. When we evaluate an expression, the value varies depending on the value used for the variable.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n2)[ohm_question]144884[\/ohm_question]\r\n\r\nIf you missed this problem, review this example.\r\n
    [latex]\\text{Evaluate }3x+4y - 6\\text{ when }x=10\\text{ and }y=2[\/latex].\r\n[reveal-answer q=\"769566\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"769566\"]SolutionThis expression contains two variables, so we must make two substitutions.\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    <\/td>\r\n[latex]3x+4y-6[\/latex]<\/td>\r\n<\/tr>\r\n
    Substitute [latex]\\color{red}{10}[\/latex] for x and [latex]\\color{blue}{2}[\/latex] for y.<\/td>\r\n[latex]3(\\color{red}{10})+4(\\color{blue}{2})-6[\/latex]<\/td>\r\n<\/tr>\r\n
    Multiply.<\/td>\r\n[latex]30+8-6[\/latex]<\/td>\r\n<\/tr>\r\n
    Add and subtract left to right.<\/td>\r\n[latex]32[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nWhen [latex]x=10[\/latex] and [latex]y=2[\/latex], the expression [latex]3x+4y - 6[\/latex] has a value of [latex]32[\/latex].\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n3)[ohm_question]142131[\/ohm_question]\r\n\r\nIf you missed this problem, review the following video.\r\n\r\nhttps:\/\/youtu.be\/_hBoWoctfAo\r\n\r\n<\/div>","rendered":"

    What you’ll learn to do: Plot points on the rectangular coordinate system and find solutions to linear equations<\/h2>\n

    \"This<\/h2>\n

    Cyclists speed toward the finish line.Which cyclist will win the race? What will the winning time be? How many seconds will separate the winner from the runner-up? One way to summarize the information from the race is by creating a graph. In this chapter, we will discuss the basic concepts of graphing. The applications of graphing go far beyond races. They are used to present information in almost every field, including healthcare, business, and entertainment.<\/p>\n

    Before you get started in this module, try a few practice problems and review\u00a0prior\u00a0concepts.<\/p>\n

    \n

    Readiness Quiz<\/h3>\n

    1)