Direct and Inverse Variation
Joint Variation
Word Probems!
Writing Linear Equations
Parallel/Perpendicular Lines
Solving Absolute Value Equations
Graphs of Absolute Values
SAT Test Questions
100
Does the equation x = 5y model direct variation, inverse variation, or joint?
Direct
100
If y varies jointly as x and z, and y = 12 when x = 9 and z = 3, find z when y = 6 and x = 15.
z = 9/10
100
The cost of producing pencils varies directly with the number of pencils produced. If the cost of producing 6,000 pencils is $400, then what will be the cost of production for 10,000 pencils?
$666.67
100
Write the slope-intercept form of the equation given:
Slope = 9/4 y-int = - 4
y = 9/4 x - 4
100
Which of the following linear equations are parallel?
a. y = 2x + 4
b. y - 2x= -1
c. y = -2x + 5
A and B
100
|−2r − 1| = 11
r = {-6, 5}
100
Write the function that represents the graph. (Slope is up 1 over 1)
g(x) = |x+3|- 6
100
Hiro and Sofia purchased shirts and pants from a store. The price of each shirt purchased was the same and the price of each pair of pants purchased was the same. Hiro purchased 4 shirts and 2 pairs of pants for $86, and Sofia purchased 3 shirts and 5 pairs of pants for $166. Which of the following systems of linear equations represents the situation, if x represents the price, in dollars, of each shirt and y represents the price, in dollars, of each pair of pants?
A) 4x + 2y = 86 3x + 5y = 166
B) 4x + 3y = 86 2x + 5y = 166
C) 4x + 2y = 166 3x + 5y = 86
D) 4x + 3y = 166 2x + 5y = 86
A) 4x + 2y = 86 3x + 5y = 166
200
Find y when x =1.5, if y varies directly as x and y =- 16 when x=6.
y = -4
200
If y varies jointly as x and z, and y = 33 when x = 9 and z = 12, find y when x = 16 and z = 22.
y = 968/9
200
6 people can do a job in 10 hours. How long will it take 9 people to do the same job?
6 hours and 40 min
200
Write the slope-intercept form of the equation of the line through the given point with the given slope.
through (4, 1), slope = 3/4
y = 3/4 x - 2
200
Write an equation for a line passing through (2,3) that is parallel to y = 5.
y=3
200
-5abs(4+n)<-15
n> -1 or n< -7
200
Graph:
y = 3|x-1| +4
(You must give me the vertex and slope of the graph)
200
The front of a roller-coaster car is at the bottom of a hill and is 15 feet above the ground. If the front of the roller-coaster car rises at a constant rate of 8 feet per second, which of the following equations gives the height h, in feet, of the front of the roller-coaster car s seconds after it starts up the hill?
A) h = 8s + 15
300
If y varies inversely with x and y = 0.3 when x = 3.5, then find the value of y when x = 3.
y = .35
300
Suppose y varies jointly with x and z. If y = 20 when x =2 and z = 5, find y when x =14 and z=8.
y = 224
300
Write the slope-intercept form of the equation of the line through the given points.
through (2, 4) and (3, 1)
y = - 3 x + 10
300
Write the linear equation it is perpendicular to the line y= -2x + 3 and the line passes through the point (-2, 4)
y = 1/2x + 5
300
|v + 8| − 5 = 2
v = {-1, -15}
300
Write the equation for the following absolute value:
g(x) = -2|x+3|
300
In the xy-plane, the graph of the linear function f contains the points (0,3) and (7,31). Which equation defines f, where y=f(x)?
A) f(x)=28x + 34
B) f(x)=3x + 38
C) f(x)=4x + 3
D) f(x)=7x + 3
C) f(x)=4x + 3
400
If y varies inversely as x and x=7 when y =21, find y when x =42.
y = 3.5
400
If p varies jointly as q and r squared, and p = 225 when q = 4 and r = 3, find p when q = 6 and r = 8.
p = 2400
400
Adult tickets for the school musical sold for $3.50 and student tickets sold for $2.50. On a given night, 321 tickets were sold for $937.50. How many of each kind of ticket were sold?
(135, 186)
adults-135
Children- 186
400
Write the slope-intercept form of the equation of the line through the given point with the given slope.
through (2, -2), slope = 0
y = - 2
400
What is the equation for a line is that parallel to y=(3/4)x+1 and has a y- intercept at -2?
y=(3/4)x-2
400
abs(2w-1)<11
-5<w<6
400
Graph (you need to give the vertex and slope of the graph):
y=-1/2abs(x-4)+3
400
A line passes through the points (2,1) and (5,12). If a new line is drawn perpendicular to the original line, what will its slope be?
-3/11
500
Y varies directly as the cube of x. If y = 1,000 when x=2, find y when x =3.
y = 3,375
500
If a varies jointly as b cubed and c, and a = 36 when b = 4 and c = 6, find a when b = 2 and c = 14.
a = 21/2
500
The volume of a can varies jointly as the height of the can and the square of its radius. A can with an 8 inch height and 4 inch radius has a volume of 402.12 in3. What is the volume of a can that has a 2 inch radius and a 10 inch height?
125.66 in3
500
Write the slope-intercept form of the equation of the line through the given points.
through (3, -1) and (4, -3)
y = - 2 x + 5
500
What is the equation of a line that is perpendicular to -3x-2y=-8 and contains the point (-9,2)?
y=(2/3)x+8
500
− 5 |5m − 5| + 2 = −73
m = {-2, 4}
500
Describe the transformations from f(x) = |x| to g(x) = (1/2)|x+2| - 5.
g(x) is down 5, shrinks, and to the left 2 from f(x)
500
The y-intercept of the graph of y = −6x − 32 in the xy-plane is (0, y).
What is the value of y ?
- 32