Expressions

Unit Review Sheet

These facts and definitions should be mastered throughout this unit. This page can be used for periodic review and study as you are finishing the unit and in the future.

Facts and Definitions

Lesson 1: Equivalent Expressions

The Commutative Property states that you can change the order of numbers in addition or multiplication without changing the answer.
The Associative Property tells us that when you use addition or multiplication, the way you group numbers doesn't change the answer.
The Distributive Property says to multiply the number outside the parentheses by each number inside.

Lesson 2: Rewriting Expressions

Sales tax is a percentage of the price of an item that is added to the final cost.
Sales Tax = Original Price × Sales Tax Rate
One-step formula for total price after sales tax: Total Price = Original Price × (1 + Sales Tax Rate)
One-step formula for discounted price: Discounted Price = Original Price × (1 − Discount Rate)
One-step formula for original price before a discount divide the discounted price by (1 minus the discount rate as a decimal).
The wholesale price is the amount you pay to buy a product from a supplier (before selling it).
The markup is the extra amount or percent added to the wholesale price so you make a profit.
One-step formula for calculating markup: Selling Price = Wholesale Price × (1 + Markup Rate)
A profit margin is a percentage of the final selling price that is profit.
Fixed costs stay the same no matter how many items you make, sell, or use.
Variable costs go up or down depending on how many items you make, sell, or use.
The formula for total price:Total Price = Fixed Cost + (Variable Cost per Item × Number of Items)

Lesson 3: Algebraic Expressions

To factor a linear expression means to pull out a number or variable that all the terms share and write the expression as multiplication. This is the Distributive Property in reverse.
The perimeter of a rectangle can be found using P = 2(l + w).
Equations in the form ax + b = c and a(x + b) = c may look similar but often lead to different solutions.
If an expression has parentheses and a multiplier, it can be helpful to distribute the multiplier across each term inside the parentheses before continuing to simplify: a(x + b) = ax + ab

Lesson 4: Graphing Proportions

A proportional relationship has a constant rate (meaning the ratio stays the same) and is represented by a straight line that passes through the origin (0, 0).
The unit rate tells you how much of something there is per one of something else.
In a proportional relationship the unit rate is found by dividing the y-value by the x-value for any given point on the line.
The constant of proportionality (k) in the equation y=kx is found by dividing y by x.
In a proportional relationship the unit rate and the constant of proportionality are the same.

Lesson 5: More Graphing Proportions

The unit rate is always the y-value when x = 1.
In the equation y = mx, m is both the slope and the unit rate.
A greater unit rate means a faster change, which appears as a steeper line on a graph.
Slope describes the steepness of a line. You can find slope in a table, a graph, or an equation.
A positive slope means the line goes up from left to right; a negative slope means it goes down from left to right.
The Two-Point Formula: $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ calculates slope from two points.
If an equation is written in the form y = mx + b, the slope is always m.

Lesson 6: Intercepts

A linear equation creates a straight line when graphed. This line will cross the x-axis and y-axis at specific points called intercepts.
The x-intercept is the point where the line crosses the x-axis.
The y-intercept is the point where the line crosses the y-axis.
The y-value is always 0 at the x-intercept.
The x-value is always 0 at the y-intercept.
To find the x-intercept, set y = 0 in the equation and solve for x.
To find the y-intercept, set x = 0 in the equation and solve for y.

Lesson 7: Rise Over Run

Rise is the vertical change (change in y).
Run is the horizontal change (change in x).
Rise over Run is used to find the slope (m).
m = rise/run = $\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .
Lattice points are points where a line crosses the grid intersections.
No matter which two points are chosen on a straight line, the slope remains the same.
When triangles are similar, the ratio of the sides is proportional.

Lesson 8: y = mx + b

Slope-intercept form is $y = m x + b$ .
In slope intercept form, b is the y-intercept.
Changing b moves the line up or down but does NOT change the slope (the tilt of the line stays the same).
A positive slope has an m > 0.
A negative slope has an m < 0.
A zero slope is a flat horizontal line (m = 0).
The slope of a vertical line is undefined.
To convert an equation into slope-intercept form, isolate y on the left side.
To find the equation from a table, determine the slope using $m = \frac{change in y}{change in x}$ , then use one point from the table and the slope to solve for the y-intercept (b) in the equation $y = m x + b$ .

Lesson 9: Unit 3 Test

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Final Project: Planes, Trains, and Automobiles

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