Review of Topics Algebra 1

Algebra 1 Review of Topics

Final Exams: January 27 and January 30

Topics we will cover today:

-Creating equations based on given situations and word problems (inequalities, linear equations, systems)

-Determining solutions from a graph

-Properties of Equality/Combining Like Terms

-Interpreting information from a graph

-Solving/Graphing Inequalities

-Interpreting Slope

Subject | Subject

You are running a concession stand at a basketball game. You are selling hot dogs and sodas. Each hot dog costs $1.50 and each soda costs $0.50. At the end of the night you made a total of $78.50. You sold a total of 87 hot dogs and sodas combined. You must report the number of hot dogs sold and the number of sodas sold. How many hot dogs were sold and how many sodas were sold?

​Example

​What variable can I use for hot dogs and what can I use for sodas?

Solving

System Word Problems

Multiple Choice

A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $4 more than the first customer for 1 large candle and 8 small candles. The price of each large candle is the same, and the price of each small candle is the same.

Which system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y?

• 4y = 3x + 64

  8y = x + 68

• 4y = 3x + 64

  8y = x + 60

• 3x + 4y = 64

  x + 8y = 68

• 3x + 4y = 64

  x + 8y = 60

Multiple Choice

On Monday Joe bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50.  It turns out that the doughnuts were more popular than the coffee.  On Tuesday he bought 5 cups of coffee and 10 doughnuts for a total of $14.25.  Which equations could be used to determine the cost of the coffee? 

• 10c + 5d = 14.25 5c + 10d = 16.50

• 10c + 5d = 16.50 5c + 10d = 14.25

• c + d = 10 5c + 10d = 16.50

• c + d = 5 5c + 10d = 16.50

Identifying Slope in a Word Problem

Remember that the slope is also the rate of change. So when you are reading a word problem, the slope is rate of change. How is what the problem is talking about changing? You will often see phrases with "per" identifying the slope: per hour, per mile, per day, etc.

Identifying Y-Intercept in a Word Problem

The y-intercept in a word problem is the starting point or starting value. As you read the word problem, ask yourself what are we starting with? That's the y-intercept.

Multiple Choice

A large pizza at Palanzio’s Pizzeria costs $6.80 plus $0.90 for each topping. The cost of a large cheese pizza at Guido’s Pizza is $7.30 plus $0.65 for each topping. Which system of equations could be used to find the number of toppings when both companies cost the same amount? 

• y = 6.80 + .65x y=7.30+.90x

• x + y = 6.80 x + y = 7.30

• y = 6.80+.90x y = 7.30 + .65x

• y + .90x = 6.80 y + .65x = 7.30

Writing and Solving Linear Inequalities

1. Five times a number n is more than 25.  Write an inequality and determine the values for number n.

2. Connor has a business that he earns $10 per video he edits.  He already has $30.  He wants to earn enough to buy a new computer for $850.  Write an inequality that represents the least number of videos he has to edit before he can buy the computer and solve.

3. Makayla wants to buy some new jeans at her favorite store.  Each pair of jeans cost $25 and she also wants to get a pair of shoes for $35.  Write an inequality that she could use to figure out how many jeans she can buy if she can spend no more than $85 and solve.

4. Antonio joins a gym that charges a monthly fee of $5 and then a $2 charge for each time he uses the gym.  Write an inequality that represents how many times he can use the gym if his monthly bill is no more than $23 and solve.

Multiple Choice

Identify the property you would use to solve this equation:
y – 7 = 28

• Additive Property of Equality

• Subtraction Property of Equality

• Multiplicative Property of Equality

• Division Property of Equality

Multiple Choice

What property of equality is used to solve y + 3 = 6?

• Addition POE

• Subtraction POE

• Multiplication POE

• Division POE

Multiple Choice

$$What\ property\ of\ equality\ is\ used\ to\ solve\ \frac{y}{3}=2$$  

• Addition POE

• Subtraction POE

• Multiplication POE

• Division POE

Multiple Choice

$$What\ property\ of\ equality\ is\ used\ to\ solve\ 3y=12$$  

• Addition POE

• Subtraction POE

• Multiplication POE

• Division POE

​Solving Inequalities

​Just like with linear equations, to solve for one inequality, we need to isolate the variable.

​

​*Note: If you divide by a negative number, the inequality symbol changes directions

​Example: 6x -3y > 15

Multiple Choice

-3 − 6(4x + 6) > -111

• x > 3

• x < 3

• x < -3

• x > -3

Multiple Choice

Solve the inequality: $$4x-2<10$$  

• $$x>3$$  

• $$x<3$$  

• $$x>2$$  

• $$x<2$$  

Multiple Choice

Solve the inequality:

$$-27-10x<23$$  

• $$x<5$$  

• $$x>5$$  

• $$x<-5$$  

• $$x>-5$$  

​Graphing an Inequalities on a number line

Let's graph the solution to y + 2 > 7

Draw

Use the number line to graph the solution to $$3+x\ge7$$  

Draw

Use the number line to graph the solution to -4x + 8 < 12

Multiple Choice

Find the slope of the line that passes through:
(-4, 7) and (-6, -4)

• 2/11

• 13/2

• 3/10

• 11/2

Multiple Choice

Find the slope of the line.

• -5/4

• 5/4

• -4/5

• 4/5

Multiple Choice

Find the slope

• -5/3

• -3/5

• 5/3

• 3/5

This is the graph of

y = 2x - 1

The next slide will identify the points we can see that fall ON THE LINE.

This is the graph of

y = 2x - 1

The points we see are:

(-2,-5)

(-1,-3)

(0,-1)

(1,1)

(2,3)

(3,5)

This is the graph of

y = 2x - 1

Let's pick a point NOT on the line.

I chose (2,1)

Let's plug it in.

y = 2x - 1

If we pick a point NOT on the line the equations ends up NOT true.

Multiple Choice

If y = -2x + 4, then (1,6) is a solution.

• True

• False

Multiple Choice

If y = -5x - 8, then (0,-8) is a solution.

• True

• False