the graphing calculator, you will need to use
several keys on the upper half of the graphing
calculator (see Figure 3.21). The upand-down
and left-and-right arrow keys are located in the
upper right corner of Figure 3.21. These are
used for moving the cur
to point Q(8, 8). Hence, the slope is still y/x
= 5/6. Consider a second example shown in
Figure 3.55. Note that the line slants downhill,
so we expect the slope to be a negative
number. 1 10 10 1 x y y = 4 x = 6 P(2, 7)
Q(8, 3) R(2, 3) Figure 3.55: Deter
keystrokes: X, T, , n 2 7 ENTER The caret
() symbol (see Figure 3.21) is located in the
last column of buttons on the calculator, just
underneath the CLEAR button, and means
raised to. The caret button is used for
entering exponents. For example, x2 is en
closely, solving for y to put each in slopeintercept form. Lets start with the equation on
the left. y 2 = 3 2 (x (1) Using m = 3/2
and (x0, y0)=(1, 2). y 2 = 3 2 (x + 1)
Simplify. y 2 = 3 2 x 3 2 Distribute 3/2. y
2+2= 3 2 x 3 2 + 2 Add 2 to both sides.
left-andright arrow keys) to delete them.
Figure 3.24: Press the Y= button to open the Y=
menu. Figure 3.25: Enter y = x + 1 in Y1=. Next,
move the cursor to Y1=, then enter the
equation y = x + 1 in Y1 with the following
button keystrokes. The result is
of 2/3. reduces to the slope of the line
through the points P and Q in Figure 3.57.
Answer: 5 5 5 5 x y P(4, 2) Q(0, 1) A
summary of facts about the slope of a line. We
present a summary of facts learned in this
section. 1. The slope of a line is the rate
points in your table. Finally, use the plotted
points as evidence to draw the graph of y = x
+ 5. 36. Use a graphing calculator to complete
a table of points satisfying the equation y = 4
x. Use integer values of x, starting at 10 and
ending at 4. Round
the line in Figure 3.49 goes downhill less
quickly than the line in Figure 3.50.
Remember, the slope of the line is the rate at
which the dependent variable is changing with
respect to the independent variable. In both
Figure 3.49 and Figure 3.50, the dep
CHAPTER 3. INTRODUCTION TO GRAPHING
Next, at time t = 0 s, the speed is v = 0 m/s.
This is the point (t, v) = (0, 0) plotted in Figure
3.42. Secondly, the rate at which the speed is
increasing is 10 m/s per second. This means
that every time you move 1 se
step is to load the equation y = x2 7 into the
Y= menu of the graphing calculator. The
topmost row of buttons on your calculator (see
Figure 3.10) have the following appearance: Y=
WINDOW ZOOM TRACE GRAPH Pressing the
Y= button opens the Y= menu shown in
seconds. Then plot a minimum of 5 additional
points using the fact that the object is
accelerating at a rate of 5 meters per second
per second. c) Sketch the line representing the
objects velocity versus time. d) Calculate the
slope of the line. 2. An obj
axis. Include units in your labels. b) Use the
initial volume of water in the tank and the rate
at which the volume of water is decreasing to
draw the line representing the volume V of
water in the tank at time t. Use the slopeintercept form to determine
the same color as the 2ND key. To open the
TABLE, enter the following keystrokes. 2ND
GRAPH The result is shown in Figure 3.15.
Note that you can use the up-and-down arrow
keys to scroll through the table. Figure 3.14:
Opening the TBLSET menu. Figure 3.15
a table of points satisfying the equation y = x3
+ 3x2 13x 15. Use integer values of x,
starting at 6 and ending at 4. After
completing the table, set up a coordinate
system on a sheet of graph paper. Label and
scale each axis, then plot the points in you
from R to Q). Thus, the slope is still y/x =
4/6, or 2/3. We can verify our geometrical
calculations of the slope by subtracting the
coordinates of the point P(2, 7) from the point
Q(8, 3). Slope = y x = 3 7 8 2 = 4 6 = 2 3
This agrees with the calculatio
y x = 8 3 8 2 = 5 6 Thus, the slope of the
line through the points P(2, 3) and Q(8, 8) is
5/6. To use a geometric approach to finding
the slope of the line, first draw the line
through the points P(2, 3) and Q(8, 8) (see
Figure 3.53). Next, draw a right t
variable. In both Figure 3.47 and Figure 3.48,
the dependent variable is y and the
independent variable is x. 190 CHAPTER 3.
INTRODUCTION TO GRAPHING Subtract the
coordinates of point P(3, 2) from the
coordinates of point Q(3, 2). Slope of first line
= y
RATES AND SLOPE 185 Now, suppose that the
evening temperature measures 50 F. To
calculate the change in temperature from the
afternoon to the evening, we again subtract.
Change in temperature = Evening temperature
Afternoon temperature = 50 F 60 F = 10
F
by 5:ZSquare from the ZOOM menu to produce
the graph shown in Figure 3.66. 10 10 10 10
x y y = 7 x = 3 (0, 2) (3, 5) y = 7 3 x + 2
Figure 3.65: Hand-drawn graph of y = 7 3x + 2.
Figure 3.66: Select 6:ZStandard from the
ZOOM menu, followed by 5:ZSquare fro
20 0 10 x y 198 CHAPTER 3. INTRODUCTION TO
GRAPHING 17. 5 5 10 10 x y 18. 10 10 5 5 x
y 19. On one coordinate system, sketch each of
the lines that pass through the following pairs
of points. Label each line with its slope, then
explain the relationship b
pronounced the change in T . 2. T is also
pronounced the difference in T . Slope as
Rate Here is the definition of the slope of a
line. Slope. The slope of a line is the rate at
which the dependent variable is changing with
respect to the independent vari
number of points that satisfy the equation y =
x + 1. In Figure 3.8, weve plotted only 13
points that satisfy the equation. However, the
collection of points plotted in Figure 3.8
suggest that if we were to plot the remainder
of the points that satisfy th
and ending at 4. After completing the table,
set up a coordinate system on a sheet of graph
paper. Label and scale each axis, then plot the
points in your table. Finally, use the plotted
points as evidence to draw the graph of y = x2
2x 3. 29. Use a grap
distance d in terms of the time t. So, to finish
the solution, replace y with d and x with t
(check the axes labels 208 CHAPTER 3.
INTRODUCTION TO GRAPHING in Figure 3.70)
to obtain a solution for part (a): d = 2t + 300
Now that our equation expresses the
final shape of the graph. If you still cannot
predict the eventual shape of the graph, keep
adding points to your table and plotting them
until you are convinced of the final shape of
the graph. Here are some additional
requirements that must be followed
the intercept (0, b), this form is called the
slope-intercept form of a line. You Try It!
EXAMPLE 1. Sketch the graph of the line
having equation y = 3 5 x + 1. Sketch the graph
of the line having equation y = 4 3 x 2.
Solution: Compare the equation y = 3
Figure 3.63. 10 10 10 10 x y y = 3 x = 5 (0,
1) (5, 4) y = 3 5 x + 1 Figure 3.62: Hand-drawn
graph of y = 3 5x + 1. Figure 3.63: Select
5:ZSquare from the ZOOM menu to draw the
graph of y = 3 5x + 1. When we compare the
calculator image in Figure 3.63 wit
MODE menu. Next, note the buttons across
the first row of the calculator, located immeThe QUIT command is located above the
MODE button on the calculator case and is
used to exit the current menu. diately below
the view screen. Y= WINDOW ZOOM TRACE
GRAPH
The direction of subtraction does not matter.
When calculating the slope of a line through
two points P and Q, it does not matter which
way you subtract, provided you remain
consistent in your choice of direction. The
Steepness of a Line We need to examin
recording onto your homework. However, we
think we would have a better picture if we
made a couple more changes: 1. It would be
nicer if the point of intersection were more
centered in the viewing window. 2. There are
far too many tick marks. With these t