Name: Date:
Student Exploration: Point-Slope Form of a Line
Vocabulary: point-slope equation, slope, slope-intercept equation, y-intercept
Prior
... [Show More] Knowledge Questions (Do these BEFORE using the Gizmo.)
1. After five days in her new job, Karen has $800 in her bank account. If she is adding exactly
$50 to her account each day, when will her balance reach $1000? Explain.
2. How much was in Karen’s account five days ago, just before she started the job?
Explain.
Gizmo Warm-up
There are many ways to define a line. One way is to state the
coordinates of a point on the line – such as (5 days, $800) – and
the rate of change of the line – such as $50/day – which is also
called the slope. You can explore how lines are graphed in this
way with the Point-Slope Form of a Line Gizmo™.
To begin, check that m, x1, and y1 are set to 1.0. (To quickly set
a slider to a specific value, type the value into the text box to the
right of the slider and press Enter or Return on your keyboard.)
1. The slope of the line is given by the variable m. Slowly drag the m slider to the right.
a) How does this change the line?
2. Set m to 2.0. Turn on the Show triangle checkbox. The triangle shows how much the
y-coordinate of the line changes (the rise) for a given change in the x-coordinate (the run). The
ratio “rise over run” is the slope of the line.
a) What is the rise?
b) What is the run?
c) What is the slope?
3. Turn off Show triangle. Drag the red point on the line to different locations on the grid.
a) How do the point’s coordinates relate to x1 and y1?
b) Does the slope change when the position of the point is changed?
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Activity A:
The point-slope
equation
Get the Gizmo ready:
· Be sure Show slope-intercept form and
Show triangle are turned off.
· Set m to 3.0, x1 to 0.0, and y1 to 0.0.
1. The point-slope form of a linear equation is y – y1 = m(x – x1). This form is most helpful
when you know the slope of a line (m) and a point on the line with coordinates (x1, y1). First, you
will work with a situation in which the point is at the origin, so (x1, y1) is (0, 0).
a) What is the point-slope equation for this line?
b) Select the TABLE tab. For each value of x, how do you calculate the value of y? [Show Less]