5.6 Connecting Variation, Slope and First Differences
Date:
The table below shows the relationship between the volume of gas remaining in a car’s fuel
tank, V, and the distance driven, D.
Distance
Driven (km)
Volume of
Fuel
Remaining (L)
0
65
100
52
200
39
300
26
400
13
500
0
First
Differences
a) Calculate the first differences.
b) What do the first differences tell you about
the relationship? List TWO things.
c) Graph the relationship on the grid
provided.
d) Calculate the slope of the relationship.
e) How could you determine the slope of the relationship
without the line?
f) What is the rate of change for this relationship?
Don’t forget to include the units.
g) Examine your graph. The vertical intercept is the point where the line touches the vertical
axis. What value is this?
What does the vertical intercept represent in this
scenario?
h) This is an example of (check one): direct variation or partial variation
Give a reason for your choice.
i) What is the fixed amount in this scenario?
j) What is the constant of variation in this scenario?
k) Write an equation for the relationship.
5.6 Connecting Variation, Slope and First Differences
What is the connection between variation, slope and first differences?
Complete the following statements:
Finite differences and the pattern in the x-values can be used to find the
the linear relation.
The
of
of variation is also the slope of a linear relation.
A constant, or average, rate of change can be interpreted as the
of a relation.
The slope of a relation can be interpreted as
.
The formulas to determine the slope of a line are:
A line has an equation of the form y = mx + b, where m represents
b represents the
and
A relation has an equation of the form y = mx + b, where m represents
b represents the
and
If a relation has a direct variation then y = mx + b can also be used, where m represents
and b =
.
The Rule of Four can be used to represent a relation in four ways…what are the four ways?
1.
2.
Homework questions:
3.
p. 284 #1,2,5,7,13,14
4.
Test Date:Fri. Oct. 31