OBJECTIVES: (List as 1, 2, etc)
1. Students will be able to discover how slope affects the graph of a line .
2. Students will be able to relate b to the y- intercept of a line .
3. Students will be able to de termine the equation of a line given m and b.
MICHIGAN BENCHMARKS:
1. Describe, analyze and generalize patterns arising in a variety of contexts
and express
them in general terms
2. Re present and record patterns in a variety of ways including tables, charts ,
graphs,
and translate between various representations.
3. Use patterns and their generalizations to make and justify inferences and
predictions.
TECHNO LOGY INTEGRATION : (List websites, software, or other computer
technology used in this lesson.)
OPENER:
Place a sign on the door that all students are to report to the computer lab.
Make sure to
bring rulers to the computer lab.
Prepare the fol lowing graphs for the students before beginning the lesson on an
overhead
projector or on a worksheet.
Summarize in your own words the following scenario:
Radar sends out a wave that bounces off an object then returns to the radar. The
radar is able to determine the distance an object is away from it at a given
time. The
radar takes several readings at slightly different times to calculate the speed
of an
object. If these readings were graphed on a time-distance graph, they may look
like
these (display the four graphs).
Ask the students which graphs show jets that are moving away from the radar.
Have
students explain why jet D is not the correct answer. Ask students which jet is
going the
fastest. Have students explain answers. Ask students which jet was the farthest
away from
the radar when the timing started. Try to lead students towards answers that
involve the
concept of slope and y-intercept. Ask students to predict the graph of a
helicopter that is
hovering 100 yards away from the radar. Discuss the various answers.
Finding the meaning of m
Instruct students to go to the right of the slope bar and type in ( one at a
time) the following
values for m: 1/3, ½, 1, 2, 4, 6. Ask students to describe the changes in
the line , as the value
of m gets larger. Now have students to type in the numbers in reverse order. Ask
students
to describe the changes in the line, as m gets closer to zero.
Now instruct students to type in some negative values for m. Ask students
how lines with
positive slope differ from lines with negative slope. Ask students to make
conjectures about
m. Students should see that m represents slope and should be able
to describe how
different values of m change the graph of a line.
Finding the meaning of ‘b’
On the y-axis of the graph is a green point. Have students drag the green point
up the y-axis
to the coordinates (0, 4). Ask students what the value of b is
next to the b slide bar. Now
have students move the green point to (0, -2). Ask the students to
explain what happened to
the value of b.
Now have students change the value of the slope to by dragging the indicator on
the slope
slide bar to the right, then to the left. Ask students what happened to the
value of b when the
slope value was changed.
Ask students to predict the value of b for the line y= -4x + 6.
Instruct students to type in the
equation for this line and check their answer. Have students make conjectures
about the
meaning of b. Students should be able to see that b represents the
y-intercept of a line.
Putting it all together
Give students the equations of several lines. Have them graph the lines on their
worksheet.
Once students complete this task, they should type in the equation for each line
and check
their answer.
Now give students the graphs of several lines and have the
students find the proper
equations. (The clipboard feature allows you to copy and paste graphs into word
processing
documents.) Have students explain their answers for each graph.
CLOSURE (and Evaluation of Student Progress):
Lines can be defined given m and b. The value of b
determines where a line crosses the y-axis.
The value of m determines the slope of the line. Both can be put together to
make an
equation for the line: y = m x + b. This form of a linear equation is
called the slope-intercept
form.
