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Algebra 1 Glencoe McGraw-Hill JoAnn Evans

Linear Functions & Graphing Using a Table of Values. Algebra 1 Glencoe McGraw-Hill JoAnn Evans. In Chapter 2 you solved linear equations . In a linear equation the exponent of the variable is one. 1.

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Algebra 1 Glencoe McGraw-Hill JoAnn Evans

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  1. Linear Functions & Graphing Using a Table of Values Algebra 1 Glencoe McGraw-Hill JoAnn Evans

  2. In Chapter 2 you solved linear equations. In a linear equation the exponent of the variable is one. 1 In this lesson you will graph linear equations in two variables. In a linear equation with two variables the exponent of the variables is one. 1 1

  3. In this lesson the equations will each have TWO VARIABLES, x and y The graph of a linear equation is the collection of all points (x, y) that are SOLUTIONS of the equation. How many points will the graph of a line contain? Way too many points to list.

  4. The graph of a linear equation is the collection of all points (x, y) that are SOLUTIONS of the equation. Today we’ll graph linear equations this way: • Make a table of values (using advantageous x-values). • Graph enough points from the table to recognize a pattern. 3. Connect the points to form a line.

  5. Graph y = 2x + 3 by constructing a table of values and graphing the solutions. Describe the pattern you notice. y x y = 2(-3) + 3 = -3 x y -3 -2 -1 0 1 ( ) -3 y = 2(-2) + 3 = -1 ( ) -1 y = 2(-1) + 3 = 1 ( ) 1 The pattern? The points all lie on a line. The ENTIRE line, even the parts not shown, is the graph of y = 2x + 3. Every point on the line is a solution to the equation y = 2x + 3. ( ) 3 y = 2(0) + 3 = 3 ( ) 5 y = 2(1) + 3 = 5

  6. Before sketching a graph, make sure your equation is in “function form”. In function form, the y is isolated, making it is much easier to construct a table of values. In function form it’s easy to substitute in values for x, the independent variable in order to find the corresponding y value. The value of y depends on x.

  7. Think of an equation in function form as a type of machine……a function machine. The function machine changes numbers. The input(the x value) enters the function machine and the function produces an output (the y value). Input thex y is the output

  8. x y -3 -2 -1 0 1 2 Input the x values to find the corresponding output values for y.

  9. y x y -3 -2 -1 x 0 1 2

  10. x y -4 -2 0 2 4 Choose x values that are even so you don’t end up with fractions when multiplying by one-half.

  11. y x y -4 -2 0 x 2 4

  12. x y -2 -1 0 1 2 Rewrite the equation in function form.

  13. x y y -2 -1 0 1 x 2 (2, 13) will be off the graph. Four points should be sufficient.

  14. Important!! When you plot the points on the graph they should lie in a straight line. These are linear equations. If the points you plot don’t lie in a straight line you have either made an arithmetic mistake when you substituted in the x values -or- you have plotted the points incorrectly! Check your work to find the mistake—don’t draw a crooked line!

  15. No graphs will be accepted if they have not been neatly and carefully drawn on graph paper with a straight edge. This is non-negotiable!

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