Transcript Rate of Change and Slope - Thomasville High School

Rate of Change
and Slope
Slope and Rate of Change

The word slope (gradient, incline, pitch) is
used to describe the measurement of the
steepness of a straight line. The higher the
slope, the steeper the line. The slope of a
line is a rate of change.
Slope is a ratio and can be expressed as:
change in y
over
change in x.
or
or
or
Slopes of a Line
What kind of slope does this line have?
positive, negative, zero or undefined?"
Positive slope
Negative slope
Zero slope
Undefined or
No slope
Example:
Consider the line y = 2x + 1

By how much has the value of y
changed between the two points
(-4,-7) and (-3,-5)? This will be a
vertical change.
Answer: 2 units
By how much has the value of x
changed between the two points
(-4,-7) and (-3,-5)? This will be a
horizontal change.
Answer: 1 unit

The slope =



For every one unit that is moved on
the x-axis, two units are moved on
the y-axis. This is true at any
location on the line.
=
=2
Example:
Find the slope of a line passing through the
points (-4,4) and (8,-2).
You have several choices:
1. You can graph the points
and "count" the vertical
changes and horizontal
changes to use in the
formula:
Slope =
Notice that to read the rise and
run for these two points, we
started at (-4,4), moved "down"
(negative) 6 units and moved
"right" (positive) 12 units.
Cont…
Find the slope of a line passing through the
points (-4,4) and (8,-2).
2. You can substitute the points directly into the
formula
m=
=
Real-World Problem Solving
Todd had 5 gallons of gasoline in his motorbike. After
driving 100 miles, he had 3 gallons left. The graph
at the right shows Todd's situation.
a. Find the slope of the line.
b. What does this slope tell us?
Since
, we know that
Todd's bike is burning .02 gallons of
gasoline for every mile that he
travels. The negative value of the
slope tells us that the amount of
gasoline in the tank is decreasing.
Cont…
c. What is Todd's mpg?
The
tells us that Todd can drive 50
miles on one gallon of gasoline (an mpg of 50 miles per
gallon).
Do these…
Find the slope of a line given two points or
graph.
1. (3, 2) and (5, 6) 2. (-4, -5) and (-9, 1)
3.
4.
Answers: 1. 2
2. -6/5 3. 2/5
4. -2
Do these…
Find the rate of change for each situation.
5. A baby is 18 in long at birth and 27 in long at ten months.
6. The cost of group museum tickets is $48 for four people and
$78 for ten people.
Find the rate of change for the data in the table or graph.
7.
8.
Tickets
Cost
5
6
7
8
$75
$90
$105
$120
Answers: 5. 9-10 in/month 6. $5/person 7. $15 per ticket
8. -100/3, value drops 100 every 3 years