Semester Exam Day 2

Semester Exam Day 2

Mr. Turrubiartes

Dec. 8, 2020

Parallel Linea & Perpendicular Lines

• Parallel Lines: Same Slope, Different y-intercept, & they never intersect each other.

• Perpendicular Lines: Different Slope (reciprocal), 90 degrees on interaction of lines.

YouTube Video

https://www.youtube.com/watch?v=P3AOoLbA3us

How do we know when two lines are parallel?

• y=3x+2

• Slopes should be the same.

Multiple Choice

Slopes of parallel lines are.....

• opposite reciprocals

• the same

• opposite

• always 5

Multiple Choice

What slope if parallel to:

m=3/4

• 4/3

• -3/4

• 3/4

• -4/3

Multiple Choice

What slope is parallel to:

m=4

• 4

• -4

• -1/4

• 1/4

How do we know when two lines are perpendicular?

• y=2/3x -3

• You need to do the opposite reciprocal of your slope.

• You need to also change the sign. If negative it will be positive and vise versa.

• Opposite Reciprocal means you flip your fraction and change the sign. Example (3/1) --> (-1/3)

Multiple Choice

Slopes of perpendicular lines are

• opposite reciprocals

• same

• opposite

• always 10

Multiple Choice

What is the slope of a line perpendicular to 5?

• 5

• -1/5

• 1/5

• -5

Multiple Choice

What is the slope of a line perpendicular to -10/3?

• -10/3

• 3/10

• 10/3

• -3/10

If you are given an equation and asked to find a parallel or perpendicular line that passed thru a specific point.

• Example: y=2x+2 with point passing threw (1,7)

Multi step linear equations on both sides.

-3 different solutions

1. solve for a variable.

2. Your variables cancel and you get a true statement

3. Your variables cancel and you get a false statement.

Multiple Choice

Solve for the problem?

3(2x+2)-3x=6+3x

• x=3

• no solution

• Infinite Solution

Multiple Choice

Solve the problem?

6(2x-6)=-7(-2x+4)

• x=-4

• No Solution

• Infinite Solution

Multiple Choice

Solve the problem?

-9-9x=-2(7+4x)

• x=4

• No Solution

• Infinite Solution

Systems of Equations By

• Elimination Method

• Substitution method

Possible Solutions

• 1. A solution (x,y)

• 2. No solution (your variables cancel and have false statement)

• 3. Infinite solution (your variables cancel and have true statement)

Used Substitution Method

Used Substitution Method

Used elimination method

Multiple Choice

Use elimination method for the following problem.

x+y=-3

5x-2y=-50

• No Solution

• Infinite Solution

• (-8,5)

Multiple Choice

Use substitution method for the following problem.

6x-3y=9

y=2x-5

• No Solution

• Infinite Solution

• (2, -3)

Writing down an equation based on the story provided.

• Read and underline important information.

• Write down your equations based on the story.

Haley and Nicole stopped at the school bookstore for extra supplies. Haley bought 8 pencils and 3 folders and spent $10.39. Nicole bought 5 pencils and 4 folders and spent $10.51. How much does a folder cost?

Fill in the Blanks

A music store sold a total of 27 used trumpets and clarinets in one month. Trumpets cost $149 and Clarinets cost $99. If total sales were $3223, write down the two equations that represent the story.

Linear Equations (slope-intercept form)

y=mx+b

• m = your slope (rise/run)

• b = your y intercept (where the line crosses on the y-axis)

Domain and Range

• Domain: is your x values (x-axis on the graph)

• Range: is your y values (y-axis on the graph)

When given a graph

-Know where you can start and end.

-If you can count or not count your stopping point.

Multiple Choice

what is the Domain values?

• $\left(-\infty,\infty\right)$

• $\left(-1,5\right)$

• $-1\le x\le5$

• $-1\le x<5$

Good Luck Tomorrow

Make sure you sleep a lot!!!

Don't forget to use Desmos!!!!