January 4th & 5th: 4.1 Getting Started with Slope
Open your books to 1. With your partner, determine which roof is the
page 309. steepest. Then write down how you might explain how
you decided which roof is the steepest to a person who
does not understand the words steep or slope. (4
2a. What are the rise and run of the gable end?
2c. What is the mathematical process we would need to
follow to find the length of each of the vertical boards?
For You to Explore: Take 4 minutes to discuss and record your ideas for Tony
and Sasha's bike trip. Be prepared to share your ideas
with the rest of the class.
3a. Who rode faster, Tony or Sasha? Explain.
3b. What does the intersection of the lines represent?
3c. How many miles did Sasha travel in an hour?
3d. How many miles did Tony travel in an hour?
Checkpoint: Draw After each equation is shown, "draw" the general
that graph! shape of the corresponding graph in the air with your
a. y =x
b. y = x2
c. y = 5x + 2
d. y = x3 + 5
e. y = 4x2 ‐ 13 + 2x ‐ 7
f. y = 2(13 ‐ 7x)
4.2 Pitch and Slope
Using pitch and slope: Pitch: Used by _________ to describe the steepness of a
Slope: Used by _____________ to describe the
steepness of a line between two points in the Cartesian
Finding the slope
Find the slope of the line that connects A(3,1) and
between 2 points:
Find two other points, S and T, such that m(S, T) is the
same as m(A, B).
Is m(S, T) = m(T, S)?
Finding slope With your partner, find the slope between the points
continued... R(7,2) and S (10,0).
Defining Slope: Given the two points A (x1, y1) and B (x2, y2):
m(A,B) = rise = y = y2 ‐ y1
run x x2 ‐ x1
Positive/ Negative Slope:
Magnitude of Slope:
Special slope cases: Find the slope between (4, 8) and (4, 2).
Find the slope between (7,2) and (3,2)
Exit Slip: Write an example of two slopes for each of the
Complete on a following statements:
with your partner. a. a positive slope and a negative slope that is steeper
b. a negative slope and a positive slope with the same
c. two pairs of points that have the same slope
d. a pair of points whose slope is undefined.