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Analyze Linear Relationships
Transcript of 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.
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.
: y value
: constant of variation (slope)
: x value
: y intercept
1. In order to draw the line, you must first find the equation using the given intercepts.
initial value "b"= 4
slope "m"= ?
2. To find the slope of the equation, you must use the formula:
3. Next, you substitute the values into the formula using the coordinates (-3,0) and (0,4) to find the slope.
Windsor Runner #1
4. Now that you have all your values, substitute the values of "m" and "b" into slope/y-intercept form:
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
equation in the question:
But, in order to draw the line, we have to change the equation from standard form to slope/y-intercept form.
5. Now that you have your equation, draw the line on a coordinate grid.
1. Change equation from standard form to slope/y-intercept form.
-6 -6 -6
2. Now that we have found the equation, we can draw the lines on the coordinate grid:
In the end, the 2 runners are running in parallel.
*the two slopes are the same:
*the y-intercepts are different:
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
By: Nour Al-Safadi and Fiza Tariq
Teacher: Mr. Byrne
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.
3. Next we will figure out the the
value using the formula
which will complete our equation
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
Shoreline slope: -3
Pathway: y= 1 x -1
Shoreline: y= -3 x+ 11
4. The lines are not perpendicular because the slopes are not negative reciprocals.
The equation for the pathway is y= 1x-1
and the equation for the shoreline is y= -3x+ 11
December 4, 2015
SPEAK OUT: Solve the following equation. Justify
6a- 2= 2a+3
CQ: What do we know about linearity?
CHOOSE A SIDE
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'
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
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?
1. Constant Rate( slope)
2. Visual: Straight line
3. Slope-intercept Form