Page 435 - Algebra 1

Math Reasoning
Write Does the inverse variation equation represent a function? Explain.
In a direct variation, if there is at least one known value for an x- and y-pair, the constant of variation, k, can be determined. The same holds true for an inverse variation; if at least one known value for an x- and y-pair exists, the constant of variation can be determined.
Graphing an Inverse Variation
Write an inverse variation relating x and y when y = 8 and x = 3. Then graph the relationship.
Example
3
SOLUTION
Find k. k = xy k = 3(8)
= 24 y = _24
Substitute in the values for x and y. Multiply.
Substitute 24 for k in the inverse variation equation. _24
Math Reasoning
Verify Explain why k can be found by multiplying the values of x and y.
x
The inverse variation relating x and y is y = x .
Use the equation to make a table of values.
Plot the points. Then connect them with a smooth curve.
Check Useagraphingcalculatortographthe equation y = _24 and to verify that your graph is
correct.
Application: Truck Transportation
A truck driver is delivering goods from one state to another. Her speed is inversely related to her travel time. If she is traveling at 55 miles per hour, it will take her 13 hours to reach her destination. How long will it take her if she travels at 65 miles per hour?
SOLUTION Use the product rule for inverse variation to solve.
x
-6
-4
-2
0
2
4
6
y
-4
-6
-12
Undefined
12
6
4
x
Example
4
Math Reasoning
Analyze Would every value in the domain and range for the function this problem represents be a reasonable solution? Explain.
420 Saxon Algebra 1
x1y1 =x2y2 55 · 13 = 65 · y2
715 = 65y2 11 = y2
Substitute 55 for x1, 13 for y1, and 65 for x2. Multiply.
Divide both sides by 65.
It will take the truck driver 11 hours if she travels at 65 miles per hour.
16
y
8
O
x
8
1
6