Graphing Linear Equations Worksheets - DOC

							Math 060 WORKSHEET                                             NAME:_________________________
3.2 Graphing Linear Equations Using Intercepts
   We graphed several equations last section. Because the graph of y  3x  2 is a line, we call it a linear
   equation. The graph of y  x 2 is not a line, so we call it a nonlinear equation. In this section we will look
   at only linear equations.
   GENERAL FORM OF A LINEAR EQUATION:
     Any linear equation can be written in the standard form:
                     Ax  By  C
       The exponents on the x and y are 1. That is why y  x 2 is not linear.

   GRAPHING LINEAR EQUATIONS:
      Since two points determine any line, it is only necessary to find two solutions to plot. The only
   problem arises if you incorrectly compute one point. We get around this by finding three points. That
   way we will notice if we incorrectly computed one of them.
   EXAMPLE: Graph each of the following:
                         y  x 1                                             8x  4 y  24
                            y                                                       y

                            x                                                       x



                                                 x                                                       x
                                                 x                                                       x




       In the second graph above, it may be easier to first solve for y and then find the solutions.
                            4 y  8 x  24
                                 8 x  24
                            y
                                   4
                                 8 x 24
                            y        
                                 4 4
                            y  2x  6

GRAPHING LINEAR EQUATIONS USING INTERCEPTS
The points where the graph crosses the axes are called intercepts.
   x  intercept: Since the value of y on the x  axis is zero, to find the x  intercept we set y  0 and
                  solve for x .

    y  intercept: Since the value of x on the y  axis is zero, to find the y  intercept we set x  0 and
                   solve for y .
                                                                                                               1
   We write the intercepts as ordered pairs since they are points.
                        x  intercept               y  intercept
                                a,0                    0, b
   It is always a good idea to plot one more point as a check.

EXAMPLE: Find the intercepts and then use them with another point to graph the line.
       a.) 7 x  3 y  6                                     b.)  4 y  5x  15



              x  intercept   __,0                             x  intercept __,0
              y  intercept   0, __                            y  intercept 0, __ 
                      y                                                 y

                      x                                                 x



                                         x                                                  x
                                         x                                                  x



                                                                            y
GRAPHING HORIZONTAL AND VERTICAL LINES
  Graph the following lines on the provided axes:                           x
          a.) x  3


          b.) y  4
                                                                                                x
                                                                                                x
          c.) y  3x




If we are graphing an equation that contains only one variable in a rectangular coordinate system, the
graph is a ______________ line or a ________________ line.




                                                                                                         2