Linear Models
To start her collection of comic books, Joylin's uncle gives her a box of comic books and several monthly subscriptions to comic books. The number of comic books in her collection, y, after x months is modeled by the equation shown:
y= 40 + 6x
What does the number 40 represent in the equation?
a) the price of a comic book subscription
b) the number of months of Joylin's subscriptions
c) the number of comic books in the box she received
d) the number of title subscriptions she receives each month
c) the number of comic books in the box she received
Solve for y:
5x - 2y = 6
y= 5/2 x -3
or
y = (6 - 5x)/-2
Solve the following system of equations:
5x + 7y = 35
y= 4x +38
Write you answer as an ordered pair.
(-7, 10)
Solve the equation:
3(2x + 7) = -16 + 19
x = -3
Write an equation for the line in the following graph:
https://docs.google.com/document/d/1uTFmEYqwIfOKRvVJPxJOkYMZvwW2VfEMI1LuImPXsjI/edit?usp=sharing
y = 4
Henry places x marbles into an empty bucket. Each marble has the same weight. The weight, in ounces, of the bucket and marbles can be calculated using the expression shown:
3x+8
What does the 3 represent in this expression?
a) the weight of each marble
b) the weight of the empty bucket
c) the number of marbles in the bucket
d) the total weight of the bucket and marbles
a) the weight of each marble
Solve the formula for the indicated variable
W = XYZ for X
X = W/(YZ)
A total of 330 children and adults attended a school play. There were 21 times as many children in attendance as there were adults.
This situation is modeled by the given system of equations, where a represents the number of adults and c represents the number of children.
c = 21a
a+c = 330
How many adults attended the play?
15 adults
Solve the equation:
7 + 4q = 8 + 3q
q=1
Write an equation for the line in slope-intercept form: (use fractions for the slope and y intercept)
https://docs.google.com/document/d/1F5S30f6gzjTZ2HRq-CoS1VEa6EaEHgG7wQRJTmO-xHA/edit?usp=sharing
y = 1/4x + 5/2
David has $400. Each week, he saves an additional $30. Write a function f(x) that models the total amount of money David has after x weeks.
f(x)= 400 + 30x
or
f(x) = 30x +400
An expression is shown:
(2x - 3) + [4x(3x + 2)]
Which expression is equivalent to the given expression?
a) 9x - 1
b) 14x + 5
c) 12x2+2x - 1
d) 12x2+10x - 3
d
What two numbers have a sum of 217 and a difference of 85?
151 and 66
Write the equation of the line passing through the points (-4,8) and (-8,4).
y = x + 12
Samantha sells two types of wristbands, rope or beaded. She charges more for the rope wristbands than the beaded wristbands. The amount of money, in dollars, that she collects from selling x wristbands of one type and y wristbands of the other type can be modeled by the expression:
5x + 8y
What does the 5 represent in the expression?
a) the number of beaded wristbands
b) the amount that she charges for the beaded wristbands
c) the number of rope wristbands
d) the amount that she charges for the rope wristbands
b) the amount that she charges for the beaded wristbands
Trent plants a sunflower that is 6 inches tall. The sunflower is expected to grow at an average rate of 1.5 inches per day during the next month.
Create an equation that Trent can use to find the number of days, x , it will take the sunflower to grow to a height of 45 inches.
45 = 1.5x + 6
y = 7x + 9
y= -3x - 11
David purchased a cell phone for $999 on a payment plan. Five months after he purchased the phone, he owed $749. Eight months after he purchased the phone, his balance was $599. Write an equation that models the amount he owes after x months.
y = -50x + 999
Stephanie adds pennies, nickels, and quarters to a scale until the mass of the combined coins is 75 grams. Each penny has a mass of 2.5 grams, each nickel has a mass of 5 grams, and each quarter has a mass of 5.7 grams.
Create an equation to model this situation, where x is the number of pennies, y is the number of nickels, and z is the number of quarters that Stephanie can put on the scale so that the combined coins is exactly 75 grams.
2.5x + 5y + 5.7z = 75
Solve the equation for x
9(x - 1) - 7 = 4x + 5(-4 + x)
No Solution
Find the equation of the line that passes through (2,12) and is parallel to the graph of y = 3x + 4. Write the equation in slope-intercept form.
y = 3x +6