partial and direct variation
DESCRIPTION
PARTIAL and DIRECT VARIATION. Recall: If a relationship is linear , its graph forms a straight line. Recall: If a relationship is linear , its graph forms a straight line. We can further divide linear relationships into two categories: direct linear relationships - PowerPoint PPT PresentationTRANSCRIPT
PARTIAL AND DIRECT VARIATION
Recall: If a relationship is linear, its graph forms a straight line.
Recall: If a relationship is linear, its graph forms a straight line.
We can further divide linear relationships into two categories:
1. direct linear relationships
2. partial linear relationships
DIRECT PARTIAL when the independent
variable is zero, the dependent variable is also zero
both sides of the equation have only one term
ex: x = 0 y = 2xy = 2(0)y = 0
DIRECT PARTIAL when the independent
variable is zero, the dependent variable is also zero
both sides of the equation have only one term
ex: x = 0 y = 2xy = 2(0)y = 0
when the independent variable is zero, the dependent variable is not zero
one side of the equation has two terms
ex: x = 0 y = 2x + 5y = 2(0) + 5y = 5
DIRECT PARTIAL value of the
dependent variable is based solely on the value of the independent variable
passes through the origin (0,0)
DIRECT PARTIAL value of the
dependent variable is based solely on the value of the independent variable
passes through the origin (0,0)
value of the dependent variable is based on both the independent variable and a constant
does not pass through the origin
Which of the following lines show:
Partial Variation?
Direct Variation?
A
B
C
Which of the following lines show:
Partial Variation?B
Direct Variation?A,C
A
B
C
1. y = 3x2. C = 200 + 4d3. a = – 70 + b 4. h = 5t
Which of the equations are partial linear relationships?
Which of the equations are direct linear relationships?
1. y = 3x2. C = 200 + 4d3. a = – 70 + b 4. h = 5t
Which of the equations are partial linear relationships?2,3
Which of the equations are direct linear relationships?1,4
We can’t use x and y intercepts alone to graph a direct linear relationship.
ex: y = 3x x-intercept: y = 0 0 = 3x0 = x (0,0)
y-intercept: x = 0 y = 3(0)y = 0 (0,0)
The x and y intercepts are the same, and we need two points to graph a line.
CALCULATING STEEPNESS WITH RATE TRIANGLES
We can also compare linear relationships based on their steepness. We determine the steepness of a line using a rate triangle.
hypotenuseheigh
t
base
Using any two points on the line as the hypotenuse, draw a right angled triangle.
The rate is a measure of steepness where:
rate = height base
6
3
Using any two points on the line as the hypotenuse, draw a right angled triangle.
The rate is a measure of steepness where:
rate = height base = 2
6
3
Determine the rate/steepness of lines A, B, and C.
A
B
C
Determine the rate/steepness of lines A, B, and C.
A
B
C
25
5
Determine the rate/steepness of lines A, B, and C.
A
B
C5
5
Determine the rate/steepness of lines A, B, and C.
A
B
C10
5
Determine the rate/steepness of lines A, B, and C.
A. r = 25 = 5 B. r = 2 = 1 C. r = 10 = 2
5 2 5
INTERPOLATION AND EXTRAPOLATION
We can use the fact that a relationship is linear to identify other data points without performing calculations.
interpolation: finding another data point that exists between two points you already know
We can use the fact that a relationship is linear to identify other data points without performing calculations.
interpolation: finding another data point that exists between two points you already know
extrapolation: finding another point that exists beyond the points you already know (extend the line)
INTERPOLATION EXTRAPOLATION