lecture 2.1 2.2a bt

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