Math EnrichmentMrs. Phillips

Agenda:• Goals• Mini Lesson• Exit Ticket

This session will be recorded for learning purposes. Learning purposes include: a lesson review for students who are absent, students who want to review for a test, etc.

EXPECTATIONS: 1.) Be respectful 2.) Participate & contribute 3.) Use your microphone 4.) 100% Attendance 5.) Be on time

Be ready to use

your microphone.

Brain Teaser :

Find the mistake in this student’s work.

Write the equation of the line through the given point with the given slope. (2, -1); m = - ½

y – 1 = - ½ (x – 2)y – 1 = - ½ x + 1

+1 +1y = - ½ x + 2-y -y

- ½ x + 2 – y

- ½ x – y + 2

How will I know if I reached my goal?

• I can answer the real world questions correctly. • I can answer my exit ticket correctly.

Goal:I can write linear equations given slope and a point on the line.

Writing Linear Equations

EXPECTATIONS: 1.) Be respectful 2.) Participate & contribute 3.) Use your microphone 4.) 100% Attendance 5.) Be on time

AI.L.6: Translate among equivalent forms of equations for linear functions, including slope-intercept, point-slope, and standard. Recognize that different forms reveal more or less information about a given situation.

Point-Slope Form

Standard Form

Ax + By + C

y – y1 = m(x – x1)

Review Formats of Linear Equations

Slope-Intercept Form

y = mx + b

m = slope

x1 = x value of given ordered pair

y1 = y value of given ordered pair

b = y-intercept (where it crosses the y-axis)

EXPECTATIONS: 1.) Be respectful 2.) Participate & contribute 3.) Use your microphone 4.) 100% Attendance 5.) Be on time

https://www.youtube.com/watch?v=Wzo5sv4IrIw&feature=youtu.be

Watch Video: How a Landfill Works2:49 Minutes

EXPECTATIONS: 1.) Be respectful 2.) Participate & contribute 3.) Use your microphone 4.) 100% Attendance 5.) Be on time

The leachate is collected through a system of pipes, moving it away from the landfill. The system’s slope changes with the shape of the land fill.

Writing Linear Equations

Vocabulary:

A leachate is any liquid that, in the course of passing through matter, extracts soluble or suspended solids, or any other component of the material through which it has passed.

EXPECTATIONS: 1.) Be respectful 2.) Participate & contribute 3.) Use your microphone 4.) 100% Attendance 5.) Be on time

C

Imagine the planners of the piping system using a coordinate graphing system to layout the slope of each pipe. If Pipe C has a slope of -3, and it falls on the point (-7, -2) on the coordinate plane, what is the linear equation for Pipe C?

Point-Slope Formula:y – y1 = m(x – x1)Writing Linear Equations

Perpendicular LinesLines that intersect to form right angles.

Slope of the purple line = -1/4

Slope of the blue line = 4/1

Conclusion?

Perpendicular lines have a negative reciprocal slope!

Check for Understanding:

Use the point-slope form to write an equation for the line that is perpendicular to the given

line and passes through the given point.

y = -1/3x + 2; (4,2)

a. y – 2 = -1/3 (x - 4)b. y – 4 = -1/3 (x – 2)c. y – 2 = 3 (x – 4)d. y – 4 = 3 (x – 2)

D

Pipe F is added for a gas collection system. It is perpendicular to Pipe D. If Pipe D has a slope of 1/3, and Pipe F falls on the point (5, -3) on the coordinate plane, what is the linear equation for Pipe F?

Point-Slope Formula:y – y1 = m(x – x1)Writing Linear Equations

Real World Question

F

Clark-Floyd LandfillBorden, IN

~130 miles from Evansville

Landfill in Southern Indiana Using a Leachate System

EXPECTATIONS: 1.) Be respectful 2.) Participate & contribute 3.) Use your microphone 4.) 100% Attendance 5.) Be on time

They need to create a new access road perpendicular to the main road as shown below. The equation for the main road is y = x + 3. The new road falls on the point (1,2) on the coordinate map. Write the linear equation for the new road.

Writing Linear EquationsReal World Question

You choose to write your answer in standard form or slope-intercept form.

Point-Slope Formula:y – y1 = m(x – x1)

A bike path for a new city park will connect the park entrance to Park Road. The path will be perpendicular to Park Road. Write an equation for the line representing the bike path.

Writing Linear EquationsReal World Practice Question #1

How can you find the slope of

Park Road?

You choose to write your answer in standard form or slope-intercept form.

Point-Slope Formula:y – y1 = m(x – x1)

The line in the graph represents the street in front of a new house. The point is the front door. The sidewalk from the front door will be perpendicular to the street. Write an equation representing the sidewalk.

How do you know the slope of the street?

You choose to write your answer in standard form or slope-intercept form.

Point-Slope Formula:y – y1 = m(x – x1)

Writing Linear EquationsReal World Practice Question #2

Reflection

2. Circle the picture that describes how you feel about today’s math problems.

I’ve been stuck all day!

I got some answers wrong.

I can do it with a little help.

Thumbs up!I get this!!

Goal:I can write linear equations given slope and a point on the line.

Writing Linear Equations

AI.L.6: Translate among equivalent forms of equations for linear functions, including slope-intercept, point-slope, and standard. Recognize that different forms reveal more or less information about a given situation.

1. Explain why you might need to use one form of a linear equation over another.

Exit Ticket

EXPECTATIONS: 1.) Be respectful 2.) Participate & contribute 3.) Use your microphone 4.) 100% Attendance 5.) Be on time

Goal:I can write linear equations given slope and a point on the line.

Writing Linear Equations

AI.L.6: Translate among equivalent forms of equations for linear functions, including slope-intercept, point-slope, and standard. Recognize that different forms reveal more or less information about a given situation.

Point-Slope Formula:y – y1 = m(x – x1)

Create an ordered pair: ( , ) Create a slope: m =

Write an equation of the line going through the above point and perpendicular to the given slope.

You Have Been Sent to a Breakout Room!

Why?

You were not meeting one of the classroom

expectations.

Send me a private chat, telling me what you will do

to improve. I will pull you back into the main room,

but you must follow the expectations to stay there.

EXPECTATIONS: 1.) Be respectful 2.) Participate & contribute 3.) Use your microphone 4.) 100% Attendance 5.) Be on time