Final Exam review

Point-Slope Form

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Point-Slope Equations need 2 things....

• A point

• A slope

Multiple Choice

Which of these is point-slope?

• $$y-y_1=m\left(x-x_1\right)$$

• $$y=mx+b$$

• $$Ax+By=C$$

Multiple Choice

Write an equation of the line going through the point (-4, 1) with a slope of 1/3.

• $$y-1=\frac{1}{3}\left(x+4\right)$$

• $$y+4=\frac{1}{3}\left(x-1\right)$$

• $$y-4=\frac{1}{3}\left(x+1\right)$$

• $$y+1=\frac{1}{3}\left(x-4\right)$$

Multiple Choice

Write the equation in point-slope form of the line that passes through the given point and has the given slope.
(4, -7); m = -1/4

• y + 7 = -1/4(x - 4)
• y - 4 = -1/4(x + 7)
• y + 7 = 4(x - 4)
• y - 7 = -1/4(x - 4)

Multiple Choice

Name the point given in this line: $$y+1=-\frac{5}{4}\left(x-3\right)$$  

• (3, 1)

• (-3, -1)

• (-3, 1)

• (3, -1)

What if I'm given just 2 points?

Multiple Choice

Write the equation in point-slope form for the line that contains the points

(-2, -3), (4, 3)

• y - 3 = 1(x - 2)

• y + 3 = 1(x + 2)

• y -3 = -1(x + 2)

• y + 3 = -1(x - 2)

We also learned how to transform Point-Slope equations into Slope Intercept form.

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Poll

Is this slope intercept form?

$$2y\ =4x\ +10$$  

• yes because it's $$y=mx+b$$  

• no, because there is a coefficient on the y.  You need to divide the entire equation by 2 first in order to get  $$y=mx+b$$  

Multiple Choice

What is the equation of the line y + 5 = -3(x - 6) in slope intercept form?

• y = -3x - 23

• y = -3x -13

• y = -3x - 11

• y = -3x+13

Multiple Choice

Two lines that are perpendicular lines have ...

• Slope that is opposite reciprocals

• No Slope

• Slope that is the same

• none of the above

Multiple Choice

Two lines that are parallel will have ...

• Slope that is opposite reciprocals

• No slope

• Slope that is the same

• none of the above

Multiple Choice

y = -2/3x + 2
y = 3/2x + 9
These lines are...

• Parallel
• Perpendicular
• Neither

Multiple Choice

y = 3x +2
y = 3x - 3
These lines are...

• Parallel
• Perpendicular
• Neither
• The same line

Multiple Choice

What is the equation of this line in slope-intercept form?

• y = 2x + 5
• y = -2x + 5
• y = -2x
• y = 5

Multiple Choice

Which equation is perpendicular to:
 y = -6x +2

• y = 6x +1
• y = 1/6x +4
• y = -6x +3
• y = -1/6x +5

Multiple Choice

Write the equation in slope-intercept form: 2x + 2y = 6

• y = - x + 3
• y = x + 3
• y = 2x +6
• y = - 2x + 6

Poll

How ready for the final exam are you?

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​Solving Multi-Step Equations

Follow along and answer the question in this Quizizz Lesson.

In case you need a little help, I have included some informational slides to help out.

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Simplifying before Solving

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As you can see in the photo to the right, some equations must be simplified before they can be solved.​

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The goal is to simplify the equation into a two-step equation.​

​The first 3 steps of this problem show how to simplify the equation.

After simplifying, we can see that ​we have a two-step equation and we use inverse operations to solve.

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If an equation contains parentheses, like the ones you see in these examples, you must distribute the value on the outside to get rid of the parentheses.

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Remember, distribute means to multiply!​

Distributive Property

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​With all POSITIVE values.

​Be careful with negatives!

Multiple Choice

5(a + 6)

• 5a + 6

• a + 30

• 5a + 30

• 5a - 30

Multiple Choice

Which of the following is equivalent to 2(c - 8)?

• 2c - 16
• 2c + 16
• 2c - 8
• c - 16

Multiple Choice

When an equation has parentheses, which operation should we use to simplify and get rid of the parentheses?

• Add

• Subtract

• Multiply

• Divide

Multiple Choice

-9(g - 3)

• -9g + 27

• 9g + 27

• -9g + -27

• -9k - 27

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Sometimes, to simplify an equation, it could involve combining like terms.

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As you can see in the example, regrouping the like terms makes it easier to combine.​

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Combine Like Terms

When combining like terms, pay attention to the sign in front of each term.

Combining could mean we add or subtract.​

Multiple Choice

Simplify the expression:

$$3a+7-2a$$  

• 8a

• 12a

• a + 7

• 5a + 7

Multiple Choice

Simplify the expression:

$$n-10+9n-3$$  

• -3
• 9n-3
• n
• 10n -13

Multiple Choice

Simplify the expression:

$$4x-3+2-2x$$  

• 6x + 5

• 2x + 1

• 2x - 1

• 6x - 1

Multiple Choice

Simplify the expression:

$$-9w+7-4w-16$$  

• -13w -9

• 5w -23

• -13w - 23

• -5w - 9

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Solving Multi-Step Equations

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​The first 3 steps of this problem show how to simplify the equation.

After simplifying, we can see that ​we have a two-step equation and we use inverse operations to solve.

​On the next few slides, you will be asked to simplify and solve a few equations. Please complete these examples on your whiteboard.

Multiple Choice

Simplify the following equation and solve for x:

$$2x-3+4x=27$$  

Show your work on your whiteboard.

• x = 12

• x = 4

• x = 5

• x = 15

Multiple Choice

Simplify the equation and solve for the variable.

$$24\ =\ 3\left(3x\ -7\right)$$

Show your work on your whiteboard.

• $$x\ =\ -9$$  

• $$x\ =\ 5$$  

• $$x\ =3$$  

• $$x\ =\ 7$$  

Multiple Choice

Simplify the following equation and solve for x:

$$3x+2(4x-4)=3$$  

Show your work on your whiteboard.

• x = 4

• x = 3

• x = 2

• x = 1

Solving Multi-Step Inequalities

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Solving Multi-step inequalities

• very similar to solving multi-step equations

• combine like terms

• get all the variables on one side
  

• isolate the variables
  
  

Multiple Choice

Solve this

$$3x+4\le19$$  

• x = 5

•   $$x\ >5$$  

• $$x\le5$$  

Multiple Choice

How would you describe the answer to the previous question?

• All numbers below 5

• All numbers above 5

• All numbers less than or equal to 5

Multiple Choice

What is the answer to this inequality?

8n-6n>24

• 
  

  $$n>12$$

• $$n<12$$

• $$n\ge12$$

Multiple Choice

Now solve 

$$16n-12\le-44$$  

• $$n\ge-2$$  

• $$n\le-2$$  

• $$n\ge2$$  

Multiple Choice

$$33\le3\left(2+3p\right)$$  

• $$p<3$$  

• $$p<11$$  

• $$p\ge3$$  

Something interesting happens when you multiply or divide both side of an inequality by a negative number.

Multiple Choice

Solve this......

$$3\left(3-3n\right)<36$$  

• $$n<-3$$  

• $$n>-3$$  

• $$n\le-3$$  

Multiple Choice

Now lets put it all together! Distribute, combine and solve!!

$$-3\left(2-3x\right)<-33$$  

• $$x<3$$  

• $$x>-3$$  

• $$x<-3$$  

Poll

How do you feel about solving inequalities now?

• Great

• Good

• Ok

• Not good