Slope and Intercept

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					Math 72                               Slope and Intercept                       Names:

Friday, we learned how to find the slope between two points. We also discovered that a
linear equation (or line) has the same slope everywhere. Below, you see graphs of lines.

   1. For each of the graphs, label 2 points on the line and find the slope between those
      two points.

                                                                        y                       y
                                          y
                                                                    3                       3
                                  3
                                                                    2                       2
                                  2
                                                                    1                       1
                                  1
                                                                                        x                       x
                                                                x           1   2   3               1   2   3
                                                1       2   3




Now we are going to look at a few other characteristics of graphs. The point where the
graph crosses the x-axis is called the x-intercept. I have labeled the x-intercept and y-
intercept on the graph below.
                    y
                                              y = 2x - 3
                3

                2

                1
                        (1.5, 0) x-intercept
                                                    x
                        1    2        3




                       (0, -3)
                    y-intercept




   2. Label the x-intercept and y-intercept on the three graphs in number 1 above. Be
      sure to give both coordinates of the points.

   3. What do you notice about the y-coordinates in each of the x-intercepts?



   4. What do you notice about the x-coordinates of the y-intercepts?
The example graph on the previous page has been labeled with the equation y = 2x-3.
We can find the x-intercept and y-intercept by simply working with this equation. To
find the x-intercept, we set y equal to zero and solve for x.

Example: Set y = 0
      0 = 2x – 3
      3 = 2x
      3                                                     3 
         x                           So the x-intercept is  ,0  or (1.5, 0)
      2                                                     2 

Similarly, we can find the y-intercept by setting x = 0 and solving for y.

Example: Set x = 0
      y = 2(0) –3
      y=0–3
      y = -3                          So the y-intercept is (0, -3)

   5. Using the above method, find the x- and y-intercepts of each of the following
      equations.
                                           1
      a. y = -5x + 35              b. y = x  6                   c. y = -13x
                                           4




   6. Make graphs of the equations in number 5 on separate axes. To make each graph,
      plot the x-intercept and y-intercept and connect them with a line.

				
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posted:10/3/2012
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