1. 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!)
2. Graphing on the Coordinate Plane
Quadrant I
(+, +)
Quadrant II
(-, +)
Quadrant IV
(+, -)
Quadrant III
(-, -)
(x, y)
3. Coordinate Points (x, y)
4. Equations of two variables
To “solve” this, we need to
find values of both x and y
that satisfy the equation.
32xy
We then write these solutions as
coordinate points (ordered pair)
5. Equations of two variables
For most multi-variable
equations, there can be an
infinite number of solutions.
32xy
6. Equations of two variables
First, can we find any
solutions to this equation?
32xy
7. Equations of two variables
Next, we need to be able to
verify if an ordered pair is a
solution to the equation
32xy
8. Equations of two variables
32xy
9. 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”
10. Sketch the Graph of
3xy
11. Sketch the Graph of
243 yx
12. 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
13. 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
14. Find the intercepts of…
1232 yx
15. Find the intercepts of…
165 2
xxy
16. Reading Graphs
17. Reading Graphs
18. 2.2a Equations of Lines
Slope – slope of a line through two
points (x1,y1) and (x2,y2) is:
m run
rise
xinchange
yinchange
12
12
xx
yy
x
y
19. 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
20. Slope-Intercept Form of a
Line (p. 90)
bmxy
Slope
of the
line
y-intercept
of the
line
21. We can use this as a graphing
technique
43xy
22. We can use this as a graphing
technique
xy 4
23. We can use this as a graphing
technique
269 yx
24. We can use this as a graphing
technique
2
5
2
3
xy
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