Intro to slope Day 1.notebook
January 23, 2017
Slope
Slope is described as the steepness of a
non-vertical line. We use the following
terms to choose the numbers:
Slope =
rise
How far up (+) or down (-)
run
How far right (+) or left (-)
Slope is known as the variable m
Slope is also referred to as rate of change.
Identify Constant and Variable Rates of Change (SLOPE)
Constant ­ the slope between any two points is always the same
Variable ­ the slope changes from one section to another.
\
Absolute
Linear
Value
Quadratic
Intro to slope Day 1.notebook
January 23, 2017
Example 1
.
.
.
.
a. Which graph is steeper? b. How would you move (spaces and directions) from one point on the graph to the other for each of Graph A and Graph B?
c. Write the numbers from part (b) as ratios, and then compare the ratios. How does this relate to which graph was steeper in part (a)?
Example 2
.
.
.
.
a. Which graph is steeper? b. How would you move (spaces and directions) from one point on the graph to the other for each of Graph A and Graph B?
c. Write the numbers from part (b) as ratios, and then compare the ratios. How does this relate to which graph was steeper in part (a)?
Intro to slope Day 1.notebook
January 23, 2017
Types of Slopes:
Positive slope
rises from left to right (left to right inclining)
Equation: y = 3x + 5
m = Zero Slope
parallel to x­axis;
slope = 0
Equation: y = 4
m = 0
horizontal line
Negative Slope
drops from left to right (left to right declining)
Equation: y = ­2x + 5
m = No Slope
parallel to y­axis; slope is undefined
Equation: x = ­6
m = NO slope or undefined
y
x
v
e
r
t
i
c
a
l
Intro to slope Day 1.notebook
January 23, 2017
What are some “real world” representations of slope? Name as many as possible.
Road Gradients
Roof pitch
Wheelchair ramps
Is it possible to ski at a 900 steepness?
What is the slope?
If a road rises 26 feet over a distance of 500 feet, what is the grade?
2 ft
5 ft
Intro to slope Day 1.notebook
January 23, 2017
Snow experts say that an avalancheis more
likely to happen if the slope is between 0.5
and 1. How about this mountain?
70 ft
200 ft
Intro to slope Day 1.notebook
January 23, 2017
Intro to slope Day 1.notebook
January 23, 2017