Solution to Additional Practice
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
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
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.