Algebra 1 Unit 2 Overview Lesson

Algebra 1 Unit 2

Overview

By Paige Roberts

Table of contents

​Solving Equations & Inequalities.........................................Slides 3 - 11

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Graphing Equations & Inequalities​....................................slides 12 - 17

​

Solving System of Equations..............................................slides 18 - 25

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​Functions & Sequences​.......................................................slides 26 - ​36

2.1 Solving Equations & Inequalities

1. Distribute.

   Multiply the 2 to everything in the parenthesis.

2. Combine like terms.

   Combine the -6 and -8

3. Isolate the variable by using Inverse Operations

   Add 14 to both sides

   Subtract 2x from both sides

   Divide by 6 on both sides.

Solving Equations

Draw

Solve the equation below. Show your work.

An inequality is like an equation, but instead of an equal sign (=), it has 1 of the 4 comparison signs.

​

We use inequalities to compare quantities.

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When we read an inequality, we read it like a book, LEFT to RIGHT.​

Inequalities

​

Solve an inequality the same way you would solve an equation.

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WHEN YOU DIVIDE OR MULTIPLY BY A NEGATIVE NUMBER, BE SURE TO TURN THE SYMBOL THE OTHER WAY.

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Solving inequalities

Draw

Solve the inequality below.

2.1 Quiz

2 Questions​

Be sure to check every question for calculator allowances.

Multiple Choice

This equation can be used to find x, the miles from Warren's house to the airport using Uber. The Uber fare was $2.10 per mile, and he gave the driver a tip of $5. Warren paid a total of $49.10.

$$2.10x+5=49.10$$  

How many miles is Warren's house from the airport?

• 7 miles

• 21 miles

• 5 miles

• 25 miles

Multiple Choice

What is the solution to the inequality $$-23-2x\ge14x-167$$  ?

• $$x\le9$$  

• $$x\ge9$$  

• $$x<9$$  

• $$x>9$$  

2.2 Graphing Equations & Inequalities

• When graphing and equation, it's important to put the equation in slope-intercept form; y = mx+b.​

• Start with the y-intercept, b.

• Then from the y-intercept, use the slope to plot another point.​

  • Positive slope will go UP AND RIGHT.

  • Negative slope will go DOWN AND RIGHT.​

​

Graphing Equations

Draw

Graph the equation below.

​When graphing inequalities, you will graph them almost the same as an equation except the line that connects the points won't always be solid. Use the chart above to correctly graph and shade the regions.

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Note: Most likely you will be able to use desmos to answer MOST of the inequality problems on your EOC.​

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GRAPHING INEQUALITIES

2.2 Quiz

1 Question​

Be sure to check every question for calculator allowances.

Open Ended

Write the inequality that is represented in the graph.

2.3 Solving System of Equations

Graphically, the solution is where the two lines intersect.

The slopes will be different.​

1 Solution

Graphically, there is no solution if the lines do not intersect (parallel lines).

The slopes are the same.​

No Solution

​

Graphically, the lines are exactly the same if the system has infinite solutions.​

Infinite Solutions

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​Replace a variable with an expression then solve.

In this example we replaced y with 24-4x in the other equation.​

​​Substitution

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​Multiply equations in order to eliminate a variable.

In this example we multiplied the bottom equation by -3 so that we could eliminate the x-terms.​

​​elimination

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• Define your variables.

• Identify your totals.

• Set up 2 equations.

• Solve the system using any method.

  Be sure that you can graph using desmos and solve using a calculator.

System Word Problems

2.3 Quiz

3 Questions​

Be sure to check every question for calculator allowances.

Multiple Choice

What is the solution to the system of equations?

• No Solution.

• (-2, 3)

• (3, -2)

• Infinite Solutions.

Multiple Choice

A grocery store sells 2-pound bags of cuties for $4 and 3-pound bags for $6. If 12 bags of cuties were sold for a total cost of $62, how many 2-pound bags were purchased?

• 4

• 5

• 6

• 7

2.4 Functions & Sequences

A relation is not a function if there is an input value that maps to different y-values.​

Example:

(0, 1), (0, -2), (1, 3), (4, -2)​, (-5, 7)

Not a Function

A function is a relation that maps each input to 1 output.​

1 x-value to 1 y-value.

Example:

(-1, 0), (0, 1), (1, 2), (2, 3), (3, 4)​

Function

Function or not

Also be able to decipher a function from a graph, a mapping and a table.

Draw

Write 4 ordered pairs that do NOT show a function.

1. ​Create a table if you see a lot of numbers in your problem.

2. Determine the slope and y-intercept.

3. Put slope and y-intercept into function form.​

​

Creating Function Rules

Draw

Create the function rule that describes the table below.

A sequence is a specific pattern.​

Sequences are very similar to functions in that they both have a rule.

Sequences can either be written explicitly or recursively.

Sequences

• Have a common difference

  • Add/Subtract by the same amount

• Can be written like a linear equation

• E​xplicit: a_n=a₁+d(n-1)

• Recursive: ​a_n=a_n-1+d

​

Arithmetic Sequences

Draw

Write the explicit and recursive rule for the following sequence below.

2.4 Quiz

2 Questions​

Be sure to check every question for calculator allowances.

Multiple Choice

Which function rule describes the table?

• $$f\left(x\right)=-7x+27$$  

• $$f\left(x\right)=7x-27$$

• $$f\left(x\right)=x-7$$  

• $$f\left(x\right)=x+27$$  

Fill in the Blanks

Don't Forget to review the topics below on your own!

• Mathematical reasoning/Algebraic justifications

• Solving literal equations

• Writing equations of lines

  • From a graph, from 2 points, from a point and a slope

• Graphing systems of inequalities

• Evaluating Functions

  • From a table, from a graph, from the function rule​

• Characteristics of Linear Functions

  • Domain, Range, Intercepts, Zeros, Inc/Dec, Pos/Neg, End Behavior​

YOU HAVE NOW COMPLETED THE OVERVIEW LESSON FOR UNIT 2!

Please complete the poll on the next slide and then complete the Unit 2 Review Questions. The answers are provided at the bottom of the last page so that you can check your work.

Poll

How do you feel you understood the lesson for unit 2?

0: I didn't understand anything from the lesson.

5: I get some of it but other things I'm still confused on.

10: I totally understood this lesson.

• 0-2

• 3-4

• 5-7

• 8-9

• 10