Inequalities
An _______ is a mathematical sentence that compares expressions. It contains the symbols >, <, ≤, or ≥.
What is an inequality?
Solve the system by graphing.
(Hint: Use 6 for the Y and X axis!)
-2x + y = 5
y = -x + 2
What is (-1, 3)?
A statement that two expressions are equal.
What is an equation?
Write the equation of this line in slope-intercept form.
(0,5) and (2,2)
What is y = -3/2x + 5?
A _________ makes a straight line when graphed.
What is a linear equation?
Write the inequality:
A number t minus 3 is at least 7
What is t - 3 ≥ 7?
Solve the system by substitution.
y = 3x - 4
5x - 2y = 10
What is x = -2 and y = -10 or (-2,-10)
2(4x - 11) = 16
What is 4.25 or 4 1/4?
Write a linear function for the following value.
f(0) = 10 and f(6) = 34
(Hint: Write in function notation!)
A __________ is a rate that describes how one quantity changes in relation to another quantity; _______ can be positive or negative.
What is a rate of change?
You booked a flight and the airline has a bag weight limit of 50 lbs. Write an inequality to represent this situation.
What is b ≤ 50 lbs?
Solve the system by elimination.
3x+2y=4
3x-2y=-4
What is (0,2)?
x - (-8) = 42
What is x = 34?
Write the equation in point-slope form, then transform into slope-intercept form.
Through (1, 2) with slope -4
What is y = -4x + 6?
You have $110 in your lunch account and plan to spend $2.75 each school day.
a. Write a linear equation that represents the balance in your lunch account.
b. How many school days will it take to spend all of the money in your lunch account? (solve for your variable)
What is y = -2.75x + 110 and 40 days?
A number n is at least -3 and less than 14.
What is -3 ≤ n < 14?
The sum of two numbers is 5. One of the numbers is 9 less than the other number. Write a system of equations and solve using substitution to determine the two numbers.
Equation 1:
Equation 2:
What is -2 and 7?
Equation 1: 2x + 5y = 100
Equation 2: y = x - 22
A rope 44 ft long is cut into 3 pieces. The first piece is 3x ft long, the second piece is 5x ft long, and the third piece is 4 ft long.
What is x = 5 5/7 ft?
What is the point slope form of the equation that passes through (-7,12) and (9,14)? Then, write in slope-intercept form.
What is y-14= 1/8x -9/8 and y=0.125x + 12.875?
Using the slope formula/an X/Y table find the slope of the line through the given points.
(4, -1) and (4,5)
What are the 2 inequality symbols that inform you it will be an OR graph?
What is >, ≥?
y=5x+1
y=5x-1
What is No Solution?
What is same slope, different y-intercept?
A rental car agency charges $30 per day plus $0.15 per mile. Another rental car agency charges $36 per day plus $0.10 per mile.
Let x = # of miles driven
Write and solve an equation to determine how many miles would have to be driven for the cost to be equal.
What is x = 120 miles?
Write the equation of the line that passes through the given point and is parallel to the given line.
(-4,2); y=1/4x +1
What is y=1/4x + 3?
You go to the store to buy shirts and pants. Shirts cost $12 each and pants cost $15 each and you have $60 to spend. 12x + 15y = 60, where x = number of shirts and y = number of pants. Given the equation in standard form, solve for the intercepts. Explain what each intercept represents.
12x + 15y = 60
What is x = 5 and 5 shirts?
What is y = 4 and 4 pants?