Linear Functions Graphing Using a Table of Values
Linear Functions & Graphing Using a Table of Values Algebra 1 Glencoe Mc. Graw-Hill Jo. Ann Evans
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
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.
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: 1. Make a table of values (using advantageous x-values). 2. Graph enough points from the table to recognize a pattern. 3. Connect the points to form a line.
Graph y = 2 x + 3 by constructing a table of values and graphing the solutions. Describe the pattern you notice. x y (-3 -3) (-2 -1 ) (-1 1) (0 3) (1 5) y = 2(-3) + 3 y x = -3 y = 2(-2) + 3 = -1 y = 2(-1) + 3 =1 y = 2(0) + 3 =3 y = 2(1) + 3 =5 The pattern? The points all lie on a line. The ENTIRE line, even the parts not shown, is the graph of y = 2 x + 3. Every point on the line is a solution to the equation y = 2 x + 3.
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.
Think of an equation in function form as a type of machine……a function machine. Input the x The function machine changes numbers. The input (the x value) enters the function machine and the function produces an output (the y value). y is the output
x y -3 -2 -1 0 1 2 Input the x values to find the corresponding output values for y.
x y y -3 -2 -1 0 1 2 x
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.
x y y -4 -2 0 2 4 x
x y -2 -1 0 1 2 Rewrite the equation in function form.
x y y -2 -1 0 1 2 (2, 13) will be off the graph. Four points should be sufficient. x
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 -oryou have plotted the points incorrectly! Check your work to find the mistake—don’t draw a crooked line!
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!
- Slides: 15