Algebra I EOC Review April 30th

Writing equations and inequalities An online movie rental company charges $25 per year to join. Members pay $1.50 for each movie they rent. Nonmembers may rent movies $3.50 each. Part A - Use the variable r to write expressions for the total cost for renting r movies for members and nonmembers. Part B – Use your expressions to determine the total coast for renting 9 movies. Part C – Write an equation to represent the point at which the cost of being a member equals the cost of being a nonmember. Then solve your equation and interpret your solution.

Writing equations and inequalities A cab company charges a flat rate of $2 plus and additional $0.50 for every mile traveled. If Sara’s cab fare was $7.50, how many miles did she travel?

Writing equations and inequalities Charles and Andrew are taking a trip to the pet store to buy some things for their new puppy. They know that they need a bag of food that costs $11, and also want to purchase some new toys that cost $3 each. Part A – If they have a total of $45 to spend, write and solve an inequality for finding the number of toys, t, they can buy. Part B – How many new toys can they buy?

Different Types of Solutions One Solution Infinitely Many Solutions No Solution

Absolute Value Equations and Inequalities 𝑥−3 =7 −5 𝑥−2 =−20 𝑥−3 >4 2𝑥 +3≥9

Literal Equations Solve for a specific variable using the same procedures as equations containing one variable. 𝑑= 𝑐 3 (𝑎−𝑏)

A relation in which each input is paired with exactly one output. Functions What is a function? A relation in which each input is paired with exactly one output.

Domain and Range Domain Range Emma’s cell phone plan charges $0.10 for each minute of talk time and a flat rate of $20 for her text messaging plan. The function f(x)=20 + .10x represents the monthly cost of her cell phone plan, wehre x represents the total numer of minutes she talks on the phone. Part A – Identify the independent and dependent variables. Part B – What is the reasonable domain? What is the reasonable range?

Slope Slope Change in y over the change in x (rise over run) Slope Formula What is the slope of the line graphed?

How quickly is the linear function increasing or decreasing. Rate of Change SLOPE!!! How quickly is the linear function increasing or decreasing.

m = slope/rate of change b = y-intercept Slope –Intercept Form 𝑦=𝑚𝑥+𝑏 m = slope/rate of change b = y-intercept For the equation, y = -8x+12, identify the slope and y-intercept. Would this line be increasing or decreasing? Explain.

Graphing from Slope-Intercept Form First, plot the y-intercept. Use your slope (rise over run) to plot more points. Connect.

Who has the greater average rate of change Who has the greater average rate of change? What does this mean in context of the problem?

Either adding or subtracting Difference is constant Arithmetic Sequences Either adding or subtracting Difference is constant Explicit Formula: 𝑎 𝑛 = 𝑎 1 +𝑑(𝑛−1) Recursive Formula: 𝑎 𝑛 = 𝑎 𝑛−1 +𝑑 Write an explicit formula for the sequence, 3, -3, -9, -15,….

Systems of Equations Two or more linear equations with the same variables. ONE soluation Solve by: Graphing Substitution Elimination

Find the solution by graphing the system. 𝑥+𝑦=6 𝑦= 1 2 𝑥−2

Find the solution by using substitution. 3𝑥−2𝑦=6 𝑥+2𝑦=10

Find the solution by using elimination. 3𝑥+2𝑦=2 5𝑥+4𝑦=6

Systems of Inequalities

Find the solution region by graphing the system. 𝑦>−𝑥+3 2𝑦+6≤𝑥