lecture 2.1 2.2a bt
TRANSCRIPT
![Page 1: Lecture 2.1 2.2a bt](https://reader035.vdocument.in/reader035/viewer/2022062405/55864fc4d8b42a713d8b46dc/html5/thumbnails/1.jpg)
Today’s Agenda
• Attendance / Announcements– Exam 1 – Tuesday 9/24• Covers Chapters 1.1 to 2.4 (skip 2.5)
• Questions from HW?• Section 2.1, 2.2a• Quiz• Have a good weekend (Go
Birds!)
![Page 2: Lecture 2.1 2.2a bt](https://reader035.vdocument.in/reader035/viewer/2022062405/55864fc4d8b42a713d8b46dc/html5/thumbnails/2.jpg)
Graphing on the Coordinate Plane
Quadrant I (+, +)
Quadrant II (-, +)
Quadrant IV (+, -)
Quadrant III (-, -)
(x, y)
![Page 3: Lecture 2.1 2.2a bt](https://reader035.vdocument.in/reader035/viewer/2022062405/55864fc4d8b42a713d8b46dc/html5/thumbnails/3.jpg)
Coordinate Points (x, y)
![Page 4: Lecture 2.1 2.2a bt](https://reader035.vdocument.in/reader035/viewer/2022062405/55864fc4d8b42a713d8b46dc/html5/thumbnails/4.jpg)
Equations of two variables
To “solve” this, we need to find values of both x and y that satisfy the
equation.
32 xy
We then write these solutions as coordinate points (ordered pair)
![Page 5: Lecture 2.1 2.2a bt](https://reader035.vdocument.in/reader035/viewer/2022062405/55864fc4d8b42a713d8b46dc/html5/thumbnails/5.jpg)
Equations of two variables
For most multi-variable equations, there can be
an infinite number of solutions.
32 xy
![Page 6: Lecture 2.1 2.2a bt](https://reader035.vdocument.in/reader035/viewer/2022062405/55864fc4d8b42a713d8b46dc/html5/thumbnails/6.jpg)
Equations of two variables
First, can we find any solutions to this
equation?
32 xy
![Page 7: Lecture 2.1 2.2a bt](https://reader035.vdocument.in/reader035/viewer/2022062405/55864fc4d8b42a713d8b46dc/html5/thumbnails/7.jpg)
Equations of two variables
Next, we need to be able to verify if an ordered pair is a
solution to the equation
32 xy
![Page 8: Lecture 2.1 2.2a bt](https://reader035.vdocument.in/reader035/viewer/2022062405/55864fc4d8b42a713d8b46dc/html5/thumbnails/8.jpg)
Equations of two variables
32 xy
![Page 9: Lecture 2.1 2.2a bt](https://reader035.vdocument.in/reader035/viewer/2022062405/55864fc4d8b42a713d8b46dc/html5/thumbnails/9.jpg)
Graphing Equations
To graph an equation in two variables is to plot the points whose ordered pairs are solutions to the equation
This can be done with a “T-Chart”
![Page 10: Lecture 2.1 2.2a bt](https://reader035.vdocument.in/reader035/viewer/2022062405/55864fc4d8b42a713d8b46dc/html5/thumbnails/10.jpg)
Sketch the Graph of3 xy
![Page 11: Lecture 2.1 2.2a bt](https://reader035.vdocument.in/reader035/viewer/2022062405/55864fc4d8b42a713d8b46dc/html5/thumbnails/11.jpg)
Sketch the Graph of243 yx
![Page 12: Lecture 2.1 2.2a bt](https://reader035.vdocument.in/reader035/viewer/2022062405/55864fc4d8b42a713d8b46dc/html5/thumbnails/12.jpg)
Intercepts
The x-intercept of a graph is the x-coordinate of where the graph crosses the x-axis
The y-intercept of a graph is the y-coordinate of where the graph crosses the y-axis
![Page 13: Lecture 2.1 2.2a bt](https://reader035.vdocument.in/reader035/viewer/2022062405/55864fc4d8b42a713d8b46dc/html5/thumbnails/13.jpg)
Intercepts
To find the x-intercept:• Set y = 0• Solve for x
To find the y-intercept:• Set x = 0• Solve for y
0,x
y,0
![Page 14: Lecture 2.1 2.2a bt](https://reader035.vdocument.in/reader035/viewer/2022062405/55864fc4d8b42a713d8b46dc/html5/thumbnails/14.jpg)
Find the intercepts of…1232 yx
![Page 15: Lecture 2.1 2.2a bt](https://reader035.vdocument.in/reader035/viewer/2022062405/55864fc4d8b42a713d8b46dc/html5/thumbnails/15.jpg)
Find the intercepts of…
165 2 xxy
![Page 16: Lecture 2.1 2.2a bt](https://reader035.vdocument.in/reader035/viewer/2022062405/55864fc4d8b42a713d8b46dc/html5/thumbnails/16.jpg)
Reading Graphs
![Page 17: Lecture 2.1 2.2a bt](https://reader035.vdocument.in/reader035/viewer/2022062405/55864fc4d8b42a713d8b46dc/html5/thumbnails/17.jpg)
Reading Graphs
![Page 18: Lecture 2.1 2.2a bt](https://reader035.vdocument.in/reader035/viewer/2022062405/55864fc4d8b42a713d8b46dc/html5/thumbnails/18.jpg)
2.2a Equations of Lines
Slope – slope of a line through two points (x1,y1) and (x2,y2) is:
mrun
rise
xinchange
yinchange
12
12
xx
yy
x
y
![Page 19: Lecture 2.1 2.2a bt](https://reader035.vdocument.in/reader035/viewer/2022062405/55864fc4d8b42a713d8b46dc/html5/thumbnails/19.jpg)
Find the slope of the lines that pass through the points…
4,58,6 and 9,23,4 and 11,42,5 and
12
12
xx
yy
m
![Page 20: Lecture 2.1 2.2a bt](https://reader035.vdocument.in/reader035/viewer/2022062405/55864fc4d8b42a713d8b46dc/html5/thumbnails/20.jpg)
Slope-Intercept Form of a Line (p. 90)
bmxy
Slopeof the
line
y-interceptof the
line
![Page 21: Lecture 2.1 2.2a bt](https://reader035.vdocument.in/reader035/viewer/2022062405/55864fc4d8b42a713d8b46dc/html5/thumbnails/21.jpg)
We can use this as a graphing technique
43 xy
![Page 22: Lecture 2.1 2.2a bt](https://reader035.vdocument.in/reader035/viewer/2022062405/55864fc4d8b42a713d8b46dc/html5/thumbnails/22.jpg)
We can use this as a graphing technique
xy 4
![Page 23: Lecture 2.1 2.2a bt](https://reader035.vdocument.in/reader035/viewer/2022062405/55864fc4d8b42a713d8b46dc/html5/thumbnails/23.jpg)
We can use this as a graphing technique
269 yx
![Page 24: Lecture 2.1 2.2a bt](https://reader035.vdocument.in/reader035/viewer/2022062405/55864fc4d8b42a713d8b46dc/html5/thumbnails/24.jpg)
We can use this as a graphing technique
25
23 xy
![Page 25: Lecture 2.1 2.2a bt](https://reader035.vdocument.in/reader035/viewer/2022062405/55864fc4d8b42a713d8b46dc/html5/thumbnails/25.jpg)
Classwork / Homework
Page 83 1 – 39 odd, 49 – 61
Page 97 1 – 31 odd