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4.2 Graphing Linear Equations

4.2 Graphing Linear Equations. Objective : To graph linear equations using a table of values. Note (1) All the Eqs. in Chap 4 refer 2 variable linear Eqs. (2) The graph of each linear eq. is a LINE. The solution to a linear equation --. is an ordered pair (x, y).

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4.2 Graphing Linear Equations

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  1. 4.2 Graphing Linear Equations Objective: To graph linear equations using a table of values. Note (1) All the Eqs. in Chap 4 refer 2 variable linear Eqs. (2) The graph of each linear eq. is a LINE The solution to a linear equation -- is an ordered pair (x, y). There are many solutions to a linear equation and all of the solutions together form a straight line, 

  2. -1 0 1 Example 1 Graph a line 8 Steps to graph a line 6 1. Pick three values for x 4 • Plug in values for x then solve for y • Solve for y, then evaluate y for all input x 3. Graph the ordered pairs 4. Connect these order pairs. This should form a straight line!

  3. Ex 2) 3x + 2y = 6 -3x -3x 2y = 6 – 3x 2 2 X y (x, y) Ex 3) Find out if the ordered pairs are solutions. HOW? A) -5x – 8y = 15 (-3, 0) B) -2x – 9y = 7 (-1, -1)

  4. Ex 4) y = -3 Ex 5) x = 4 Ex 6) x = -2 Ex 7) y = 0 Special Linear Equations always a vertical line x = #  always a horizontal line y = #  MEMORIZE THESE!!!!

  5. -1 0 2 When an equation is solved for y = Function form  What are the advantages of putting the equation into function form? You only have to solve for y once! Ex 8) Graph the given linear equations. A) 3x – y = 2 -5 -2 4 Solve for y, we get We select three x values, and evaluate the corresponding y values.

  6. -5 0 5 Ex 8) Graph the given linear equations. B) 2x – 5y = 10 -4 -2 0 Solve for y, 2x - 5y = 10 -2x -2x -5y = 10 – 2x -5 -5 We select three x values, and evaluate the corresponding y values.

  7. -3 0 3 Exmaple 9 Make a table of values and graph the following line: 2x – 6y = 12 -3 -2 -1 Solve for y, we get We select three x values, and evaluate the corresponding y values.

  8. Summary • A two variables linear equation represents a line in x-y coordinate plan. • An ordered pair is a solution to a two variable linear equation, then the point represented by the ordered pair is on the line represented by the linear equation, and vice versa. • Remember the two types of special line by an easy way: • x = #  no y  parallel to y-axis • y = #  no x  parallel to x-axis

  9. Summary • When graphing a linear equation, remember the 4 steps: • Pick a few x values • Solve for y, then evaluate y for all input x • Graph ordered pairs • Connect ordered pairs with a line

  10. Assignment P. 214 #'s: 12 - 50 (even), 52-56, 62 - 66 (even), 67-70, 76, 77

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