**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

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

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