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[A] Select the line; then, in the Measure
Menu, choose Slope.
[B] Select point E; then, in the Measure
Menu, choose Coordinates.
[C] Select the line; then, in the Measure
Menu, choose Equation.
[D] Select the equation; then, in
the Edit Menu, choose Action Button: Hide/Show.
[E] Using the Text tool,
double-click on a button to change its label. |
Lines can be described in many ways;
they are straight paths that extend forever, they can be a collection of points that
follow a certain pattern, or they can be relationships that can be described with an
equation Often the points used to describe lines have designated x- and y-coordinates,
which means that the rules for their pattern can be described in terms of two variables -
x & y. In this activity, you’ll investigate relationships between pairs of lines,
their equations and how to tell if lines are parallel or perpendicular by the equations
that describe them.
Sketch and Investigate
In the GRAPH menu,
choose Show Grid.
Then, construct line (not a segment) AB so that
neither point A nor B lies on an axis.
Construct point C at
the intersection of AB and the y-axis.
Use
GSP to Measure the Slope. [A]
Drag one of the points A or B and look
how the slope of the line changes.
Measure
the coordinates of point C. [B]
Measure
the line's equation. [C]
Drag points A and B and the line
itself, observe the three measurements. Following this observation, record your to answer
# 1 from "points to ponder".
Select
the equation and make a pair of Hide/Show action buttons. [D]
Double-click on the buttons to see how
they work.
Change
the button names from "Hide" and "Show" to "Hide Equation"
and "Show Equation".[E]
Then with the equation hidden, drag
your line to a new position and predict its new equation.complete the table in the
"Things to Do" Section.
Points to Ponder . . .
A Linear equation is in slope-intercept form if it looks like
this:
where m and b are specific values. Describe what m and b
represent, using the observations from your sketch.
Things to Do . . .
- Complete this table:
| Equation Prediction |
Correct Equation (or check) |
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Going Further & Deeper . . .
- Measure the equation of a line in slope-intercept form, then use the Graph menu to
switch your equation to Standard Form. Write down both forms of the equations and showing
your work, use algebra to demonstrate that the equations are equivalent. When you do this,
remember that the computer first rounds most of its measurements, so decimals may be
slightly different!
- Suppose a pair of parallel lines have y-intercepts that are two units apart. Does this
mean that the lines are two-units apart from each other? Construct a pair of these lines
to investigate the question. Explain how the distance between these parallel lines depends
on their slopes.
Apply what you've learned . . .
Complete assignment on Writing Linear Equations that Mr. M will give you.
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