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Algebra 1: Word Problems with direct and inverse variations
3/15/16
WARM UP
1. Write out all the equations related with direct and inverse variation.
Direct
Inverse
Equation 1: _____________________
_________________________
Equation 2: _____________________
_________________________
Equation 3: _____________________
_________________________
2. Identify the following as direct variation, inverse variation, or neither.
(a)
(c)
(e)
answer: _____________
answer: _______________
answer: ____________
(b)
answer: _____________
(d)
answer: _______________
(f) (3, 2), (6, 1),
answer: _______
____
3. Which tables below represents a direct variation table?
a
c
b
d
CLASS WORK/HOMEWORK
4. Plot 3 more points on the graph below to create a direct variation graph.
5. H varies inversely as J. When J = -4, H = 9. Find J when H = 6.
answer: ________________________
____
____
____
6. If T varies directly as W. When T = -6, W = 12. What is the value of W when T = 8?
a
-16
b
12
c
6
d
-8
7. A varies inversely as B. When A = 18, B = 4. Find B when A = 9.
a
8
c
b
12
d
8. A relationship exists between the distance, d (in miles) a car can cover and the number of gallons og
gas, g, it consumes.
* A car covering a distance of 105 miles consumes 3 gallons of gas.
* A car covering a distance of 280 miles consumes 8 gallons of gas
* Let d represents the distance in miles.
* Let g represents the gallons of gas consume.
Which statement is true about this relationship?
a
The distance varies inversely with the gallons of gas consumed because
.
The distance varies directly with the gallons of gas consumed because
.
c
The distance varies inversely with the gallons of gas consumed because
.
d
The distance varies directly with the gallons of gas consumed because
b
.
9. The width of a box varies directly with its length. If the length is 18 inches, the width is 6 inches.
What is the length of a box with a width of 24 inches?
answer: _________
10. (a) Graph
11.
(b)
____ 12.
Which expression(s) below is/are modeled by the algebra tiles above?
a
c
b
d
13. Write the equation of the line passing through the points (-4, -5) and (4,1).
slope-intercet form: ___________________
14. Graph
by finding x-intercept and y-intercept.
x-intercept = _________
____ 15.
y-intercept = ________
What is the equation of the graph below?
a
b
____ 16. A line has a slope of
c
d
and passes through the point
line? (MORE THAN ONE ANSWER)
a
(3, -10)
c
(2, -2)
b
(2, )
d
(0, -3)
. Which of the following points lie on the
____ 17. Which line(s) is/are parallel to
?
a
b
c
d
8y=-4x-16
____ 18. Which line below is perpendicular to
?
a
b
c
d
19. Which choices below is true for
? (MORE THAN ONE ANSWER)
____ 20. A vertical line passes through the point (4, -7). What is the equation of this line?
a
x = -7
c
y = -7
b
x=4
d
y=4
21.
Graph y = -4: the slope is ________________.
____ 22. A function h(x) is described as
.
* the domain of h(x) is all real numbers greater than 0.
* The range of h(x) is all real numbers less than or equal to ____________ .
a
3
b
-2
23. Write equations for the given graph
equation 1: __________________
equation 2: __________________
c
-1
d
5