Slope & Y-Intercept
In Context
Learning Goal #2 for Focus 4 (HS.S-ID.C.7, 8 & 9, HS.S-ID.B.6, HS.F-IF.B.6):
The student will be able to interpret linear models
.
4
3
2
1
0
In addition to
level 3.0 and
above and
beyond what was
taught in
class, the
student may:
· Make
connection with
other concepts
in math
· Make
connection with
other content
areas.
The student will be able
to interpret linear models.
- Interpret slope in
context of data.
- Write the line-of-bestfit for a scatter plot.
- Distinguish between
correlation and causation.
- Use technology to
calculate correlation
coefficient.
The student
will be able to:
- Determine if
a scatter plot
has positive or
negative
correlation and
if the
correlation is
weak or strong.
- Use the
correlation
coefficient to
interpret the
strength of a
correlation.
With help
from the
teacher, the
student has
partial success
interpreting
linear models
or scatter
plots.
Even with help,
the student has
no success
understanding
the concept of
a linear
models.
Using Slope-Intercept Form
• In a real-life context the y-intercept often represents an
initial amount and the slope often represents a rate of
change.
• Knowing this structure can help you understand
equations, write equations in slope-intercept form and
understand graphs.
Buying A Computer
• You are buying a computer on layaway. You make a
$250 deposit and then make weekly payments.
• The equation A = 850 – 50T represents this situation.
•
•
•
•
•
Image from
http://pixabay.com/en/computer-hardwarekeyboard-modern-156513/
What is the slope? -50
What does it mean in this situation?
What is the y-intercept? (0, 850)
What does it mean in this situation?
What is the original amount of the computer?
$1,100 [850 + 250 deposit]
Access Ramps
• Wheelchair access ramps must be built according to very
precise specifications so that the ramps are not too steep to
maneuver a wheel chair.
• If one is standing at the top of the ramp, y stands for the
height above the ground and x stands for the horizontal
distance from the start of the ramp to the platform.
• The equation for the ramp is y = 1/12 x
y = 1/12x
• What is the meaning of the y-intercept in this particular
situation?
• Suppose you wish to build a wheelchair accessible ramp
into a building, and the first floor is 4 feet above the
ground. Determine the how far out horizontally from the
building should the ramp begin?
(x, 4)
(0, 0)
Wheelchair Access Ramp
• y = 1/12x
• 4 = 1/12x
• 48 = x
• The ramp will need to
be 48 feet long.
Image from http://wheelchairassistance.com/wheelchair-ramp/trifold-wheelchair-ramps.php