Unit 1: Analyzing Lines on a Graph

In the graph below, the straight line S is given by the equation y = c + dx. If the line shifts from this initial position S0 to a new position of S1, what must have changed in the equation?

• In this graph, the line has changed in steepness, which means the slope must have changed.
• In the equation y = c + dx, "d" is the slope of the line. Since the slope must have changed, the constant "d" must have changed. Since S1 is steeper than S0 , "d" must have increased. and "c" is the y-intercept.
• In the equation y = c + dx, "c" is the y-intercept. In the graph, the lines have not been extended to where they intercept the y-axis, so it is hard to tell if "c" changed or not. Unless you extend the lines to the y-axis and can be certain the two lines both intercept the y-axis in the same place, it is hard to tell if "c" changed or not, but we can be certain that "d" did change.
• If you do extend both lines through the y-axis, you will find they have the same y-intercept, which means "c" does not change.

If you feel comfortable with this material, move on to the next unit.

IMPORTANT: If you still do not understand this practice, you may need more review than is offered by this book. You may wish to review Book I of this series before moving on.