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Analyze Linear Relationships

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Mitsouka Jean-Claude

on 20 July 2017

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Transcript of Analyze Linear Relationships

Unit 5 Assignment- Analyze Linear Relationships
Problem 1 - Question
A boat is traveling from Point D (-3,-2) towards Point C (3,1). The shoreline is a represented by the line through Points A (-1, 7) and B (5, -2) . Determine whether the path from C to D is perpendicular to the shoreline. Find the equation for the path taken and the shoreline.

Important Information
Problem 2- Question
Two runners are running on paths on opposite sides of the Detroit River. The Windsor runner is running on a sidewalk that has an x-intercept of -3 and a y-intercept of 4. On the Detroit side, there is a sidewalk that can be modeled by the equation 8x-6y-18=0. Are the two runners running on parallel paths? Show you work, and graph your solution.
Terminology
y
: y value
m
: constant of variation (slope)
x
: x value
b
: y intercept
Solution
1. In order to draw the line, you must first find the equation using the given intercepts.

x-intercept= -3
y-intercept= 4
initial value "b"= 4
slope "m"= ?

2. To find the slope of the equation, you must use the formula:
Continuation...
3. Next, you substitute the values into the formula using the coordinates (-3,0) and (0,4) to find the slope.
m= 4-0
0-(-3)
m= 4
3
Next...
Windsor Runner #1
4. Now that you have all your values, substitute the values of "m" and "b" into slope/y-intercept form:
y=mx+b
y= 4x+4
3
What's 9+10...
Solution: Part 2
Windsor Runner #2
Now that we have the equation for runner #1, we must find the equation for runner #2 by using the
standard form
equation in the question:
8x-6y-18=0
But, in order to draw the line, we have to change the equation from standard form to slope/y-intercept form.
Finally...
5. Now that you have your equation, draw the line on a coordinate grid.
y= 4x+4
3
Equation:
Solution
21
1. Change equation from standard form to slope/y-intercept form.
8x-6y-18=0
8x-8x-6y-18=0-8x
-6y-18=-8x
-6y-18+18=-8x+18
-6y=-8x+18
-6 -6 -6
y=4x-9
3 3

y=4x-3
3
Last Step
2. Now that we have found the equation, we can draw the lines on the coordinate grid:
Runner #1:
y=4x+4
3
Runner #2:
y=4x-3
3
Conclusion
In the end, the 2 runners are running in parallel.

*the two slopes are the same:
4x 4x
3 3

*the y-intercepts are different:
4 -3

What we know:
shoreline- point A (-1,7) to point B (5,-2)
boats travel- point D (-3,-2) to point C (3,1)
perpendicular lines have negative reciprocal slopes
ex. 3/2 and -2/3
equations will follow the
y=mx+b
formula




Solution
Pathway:


m= -2-1
-3-3
m= -3
-6
m= 1
2


By: Nour Al-Safadi and Fiza Tariq
Teacher: Mr. Byrne
Period: 3

1. To begin me must figure out the equation for both the shoreline and pathway. To this we must figure out the slope by using the formula below.
Shoreline:


m= 7+2
-1-5
m= 9
-6
m=-3
2





Solution

3. Next we will figure out the the
b
value using the formula
y=mx+b
which will complete our equation

So...
2.The lines are not perpendicular as the lines do not meet at a 90 degree angle and the slopes are not negative reciprocals.
Pathway slope: 1
2

Shoreline slope: -3
2
PERPENDICULAR
Pathway:
y=mx+b
-2=1(-3)+b
2
-2=-3+b
2
-2+3=b
2
-4+3=b
2 2
-1=b
2
Shoreline:
y=mx+b
7=-3(-1)+b
2
7=3+b
2
7-3=b
2
14-3=b
2 2
11=b
2




The Equations
Pathway: y= 1 x -1
2 2
Shoreline: y= -3 x+ 11
2 2
In Conclusion
4. The lines are not perpendicular because the slopes are not negative reciprocals.
The equation for the pathway is y= 1x-1
2 2
and the equation for the shoreline is y= -3x+ 11
2 2





2 2
December 4, 2015
SPEAK OUT: Solve the following equation. Justify
6a- 2= 2a+3

CQ: What do we know about linearity?
CHOOSE A SIDE
Equation 1:
5=2x- 3
Equation 2:
y=2x-3
Agree or disagree or unsure. Are these equations the same? Explain your reasoning . If you are unsure pose a question
X- independent variable
Y- the dependent variable
December 7, 2015
CQ: What is unique about linearity?
SPEAK OUT: Please take out the HW(the complete table and the question)
CQ: What do we know about linearity?
December 8, 2015

SPEAK OUT: Complete Question 29, June 14'
CQ:
What do we know about linearity?
DECEMBER 9, 2015
CQ: What do we know about linear relationship?
SPEAK OUT: Write an equation for the linear relationship below
You are given 4 representations of linear relationship. Your job with a partner is find the missing three of Situation:

Note: Description : Written representation
NEXT ACTIVITY
DECEMBER 15, 2015
SPEAK OUT: Write at least 3 facts you know about linearirty. Be sure to give an example where necessary.
CQ: How do you solve system of equations graphically?
FACTS
1. Constant Rate( slope)
2. Visual: Straight line
3. Slope-intercept Form
Y=mx+b
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