Linear Equations: y = mx + b - GeoGebra Dynamic Worksheet

Systems of 2 Linear Equations

Prof. Battaly, College Algebra

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The blue line shown on the graph has the equation y = mx + b
The sliders represent values for the slope m and the y-intercept b.
What happens to the line when you move the sliders (change the values of m and b)?
(Note that you can click on the dot on the slider and use the arrow keys on your keyboard to get changes of 0.1 on the slider.)

In the Algebra window at left, click on the line L2, the y-intercept B, and the slope M for a second line, all in red. Move the sliders for these to see that they work in the same way as those for L1 above.

1. The solution for a system of 2 lines includes all points that satisfy both equations (or the points in common on both graphs).

2. Arrange the lines so L1 is the equation y = x + 1 and
                                        L2 is the equation y = - 2x - 2
    What is the solution for this system? _______________

3. Can you arrange the lines so there are no points in the solution? ______
     What can you say about such a system? _______________

4. Arrange the lines so L1 is the equation y = 2x + 3 and
                                        L2 is the equation y = - 0.5x - 2
      What is the solution for this system? _______________
      What can you say about such a system? _______________

4. Click on all the components in the Algebra window so they are not displayed.
Try entering your homework problems in the bottom window, and finding solutions.

Answers
2. (-1,0) or x=-1, y=0
3. Yes.
     Parallel lines have equal slopes.
4. (-2,-1) or x=-2, y=-1
     The lines are perpendicular. (Note that the slopes are negative reciprocals.)