lecture 2.1 2.2a bt
TRANSCRIPT
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!)
Graphing on the Coordinate Plane
Quadrant I (+, +)
Quadrant II (-, +)
Quadrant IV (+, -)
Quadrant III (-, -)
(x, y)
Coordinate Points (x, y)
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)
Equations of two variables
For most multi-variable equations, there can be
an infinite number of solutions.
32 xy
Equations of two variables
First, can we find any solutions to this
equation?
32 xy
Equations of two variables
Next, we need to be able to verify if an ordered pair is a
solution to the equation
32 xy
Equations of two variables
32 xy
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”
Sketch the Graph of3 xy
Sketch the Graph of243 yx
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
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
Find the intercepts of…1232 yx
Find the intercepts of…
165 2 xxy
Reading Graphs
Reading Graphs
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
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
Slope-Intercept Form of a Line (p. 90)
bmxy
Slopeof the
line
y-interceptof the
line
We can use this as a graphing technique
43 xy
We can use this as a graphing technique
xy 4
We can use this as a graphing technique
269 yx
We can use this as a graphing technique
25
23 xy
Classwork / Homework
Page 83 1 – 39 odd, 49 – 61
Page 97 1 – 31 odd