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Graphing Linear Equations

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❶The components of an ordered pair x, y associated with a point in the plane are called the coordinates of the point; x is called the abscissa of the point and y is called the ordinate of the point. It is often easier to obtain solutions if equations are first expressed in such form because the dependent variable is expressed explicitly in terms of the independent variable.

7.1 SOLVING EQUATIONS IN TWO VARIABLES

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When you are given 2 equations in the same question, and asked to solve for a unique answer, you can visualize the problem as be two lines on the same xy-plane. The following two equations are graphed on the same xy-plane:. The solution set to any equation is the place where BOTH equations meet on the xy-plane. This meeting place is called the Point of Intersection. Here's a geometric view:. To solve graphically, it is best to write BOTH equations in the slope-intercept form or in the form: Then, graph the two lines, leading to the point of intersection.

After graphing these lines, you'll find that BOTH equations meet at point 0, Here's what these two equations look like on the xy-plane:. I will solve for y.

I will use our second equation. Coordinate Look at Pythagorean Triples. The site gives a small applet exploring the relationship between circles centered at the origin, linear equations, and pythagorean triples. Gives a detailed explanation of how to use interval notation, followed by numerous examples, from very simple to quite complex. This site provides graphing tools. The GCalc 3 menu has several options for graphing. One nice aspect of this site is that multiple functions can be graphed in different colors on the same screen.

Another useful feature is that it is easy to copy and paste or print the graphs that are generated. For more information call us at: Online Scientific Calculator A helpful scientific calculator that runs in your web browser window. Coordinate Look at Pythagorean Triples The site gives a small applet exploring the relationship between circles centered at the origin, linear equations, and pythagorean triples. Interval Notation Gives a detailed explanation of how to use interval notation, followed by numerous examples, from very simple to quite complex.

Online Graphing Calculator This site provides graphing tools.

7.2 GRAPHS OF ORDERED PAIRS

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The first portion of the book is homework help graphing linear equations investigation of functions – and revisited throughout. In addition to the paper homework sets, an emphasis is placed on motivating the concepts and on modeling and interpretation.

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Graphing Linear Equations Linear equations: Linear equations are nothing but algebraic equations in which each term has either a real constant or the product of a real constant other than zero and a single variable involved in the equation.

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To graph a linear equation, we can use the slope and y-intercept. Locate the y-intercept on the graph and plot the point. From this point, . The solution set to any equation is the place where BOTH equations meet on the xy-plane. This meeting place is called the Point of Intersection. If you have a linear equation and a quadratic equation on the same xy-plane, there may be TWO POINTS where the graph of each equation will meet or intersect.

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For example, an equation such 3x +5y = 16 is already in standard form, as a equals 3, b equals 5, and c equals Similarly, an equation such as y = 5x – 3 can be put in standard form as -5x +y = Graphing Linear Functions. If the equation for a function can be written in standard form, it can be graphed as a linear function. Suppose the . Systems of linear equations can be solved by other methods than graphing, such as substitution and elimination. When solving by elimination, some systems can be solved by addition, subtraction, and multiplication.