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