We will assign a number to a line, which we call slope, that will give us a measure of the "steepness" or "direction" of the line.
Systems of Equations and Inequalities In previous chapters we solved equations with one unknown or variable. We will now study methods of solving systems of equations consisting of two equations and two variables.
Represent the Cartesian coordinate system and identify the origin and axes. Given an ordered pair, locate that point on the Cartesian coordinate system. Given a point on the Cartesian coordinate system, state the ordered pair associated with it.
We have already used the number line on which we have represented numbers as points on a line. Note that this concept contains elements from two fields of mathematics, the line from geometry and the numbers from algebra.
Rene Descartes devised a method of relating points on a plane to algebraic numbers. This scheme is called the Cartesian coordinate system for Descartes and is sometimes referred to as the rectangular coordinate system.
This system is composed of two number lines that are perpendicular at their zero points.
Perpendicular means that two lines are at right angles to each other. Study the diagram carefully as you note each of the following facts. The number lines are called axes. The horizontal line is the x-axis and the vertical is the y-axis. The zero point at which they are perpendicular is called the origin.
Positive is to the right and up; negative is to the left and down. The arrows indicate the number lines extend indefinitely. Thus the plane extends indefinitely in all directions.
The plane is divided into four parts called quadrants. These are numbered in a counterclockwise direction starting at the upper right. Points on the plane are designated by ordered pairs of numbers written in parentheses with a comma between them, such as 5,7.
This is called an ordered pair because the order in which the numbers are written is important. The ordered pair 5,7 is not the same as the ordered pair 7,5.
Points are located on the plane in the following manner. First, start at the origin and count left or right the number of spaces designated by the first number of the ordered pair. Second, from the point on the x-axis given by the first number count up or down the number of spaces designated by the second number of the ordered pair.
Ordered pairs are always written with x first and then y, x,y. The numbers represented by x and y are called the coordinates of the point x,y. The first number of the ordered pair always refers to the horizontal direction and the second number always refers to the vertical direction.
Check each one to determine how they are located. What are the coordinates of the origin? Find several ordered pairs that make a given linear equation true. Locate these points on the Cartesian coordinate system. Draw a straight line through those points that represent the graph of this equation.
A graph is a pictorial representation of numbered facts. There are many types of graphs, such as bar graphs, circular graphs, line graphs, and so on.Number lines help make graphing the union of two inequalities a breeze! This tutorial shows you how to graph two inequalities on the same number line and then find the union.
Check it out! May 20, · This feature is not available right now. Please try again later. And once you have your second point you can just draw a line through the two points and extend it in both directions.
You can check to see that the line you've drawn is the correct one by substituting the coordinates of the second point into the original equation. Improve your math knowledge with free questions in "Write inequalities from graphs" and thousands of other math skills.
Write a compound inequality that the graph could represent. Download png. Ask for details A compound inequality contains at least two inequalities that are separated by either "and" or "or".
[-1, 3) The graph of the compound inequality represents the intersection of the graph of the inequalities. 0 votes 0 votes Rate! Rate! Thanks /5(4).
Larry graphs the inequality mcjpg using the steps below. Step 1: Draw a number line, and place an open circle at Step 2: Shade to the left of -5 to represent less than