2.2: Do Now: Determine if the following point is on the graph. 1.) 2.)
-
Upload
ashlie-dawson -
Category
Documents
-
view
218 -
download
0
Transcript of 2.2: Do Now: Determine if the following point is on the graph. 1.) 2.)
![Page 1: 2.2: Do Now: Determine if the following point is on the graph. 1.) 2.)](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649e7e5503460f94b8253f/html5/thumbnails/1.jpg)
2.2: Do Now: Determine if the 2.2: Do Now: Determine if the following point is on the graph.following point is on the graph.
1.)
2.)
)2,2(;62 yx
)4,1(;13 2 yx
![Page 2: 2.2: Do Now: Determine if the following point is on the graph. 1.) 2.)](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649e7e5503460f94b8253f/html5/thumbnails/2.jpg)
Academy Algebra Academy Algebra IIII
2.2: Graph of Equations in Two Variables; Intercepts; Symmetry
HW: p.171-172 (12, 18, 27, 39, 42, 45, 51-54 all)
![Page 3: 2.2: Do Now: Determine if the following point is on the graph. 1.) 2.)](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649e7e5503460f94b8253f/html5/thumbnails/3.jpg)
Graph the equation. Graph the equation. (By hand & on calculator.)(By hand & on calculator.)
1.) 2.) 52 xy 2xy
![Page 4: 2.2: Do Now: Determine if the following point is on the graph. 1.) 2.)](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649e7e5503460f94b8253f/html5/thumbnails/4.jpg)
Find the x-intercept(s) and Find the x-intercept(s) and y-intercept(s) of the graph.y-intercept(s) of the graph.
1.) 2.)42 xy 273 xy
![Page 5: 2.2: Do Now: Determine if the following point is on the graph. 1.) 2.)](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649e7e5503460f94b8253f/html5/thumbnails/5.jpg)
SymmetrySymmetrya.) A graph with b.) A graph with c.) A graph withx-axis symmetry y-axis symmetry origin symmetryfor every (x,y) the for every (x,y) the for every (x,y) thepoint (x,-y) is also point (-x,y) is also point (-x,-y) is alsoon the graph. on the graph. on the graph.
![Page 6: 2.2: Do Now: Determine if the following point is on the graph. 1.) 2.)](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649e7e5503460f94b8253f/html5/thumbnails/6.jpg)
Test SymmetryTest Symmetrya.) To test for symmetry with respect to the x-axis, replace y with –y and simplify. If an equivalent equation results, then the graph has x-axis symmetry.
b.) To test for symmetry with respect to the y-axis, replace x with –x and simplify. If an equivalent equation results, then the graph has y-axis symmetry.
c.) To test for symmetry with respect to the origin, replace x with –x and y with –y and simplify. If an equivalent equation results, then the graph has origin symmetry.
![Page 7: 2.2: Do Now: Determine if the following point is on the graph. 1.) 2.)](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649e7e5503460f94b8253f/html5/thumbnails/7.jpg)
Academy Algebra Academy Algebra IIII
2.2: FinishHW: p.172 (56, 59, 61, 68)
![Page 8: 2.2: Do Now: Determine if the following point is on the graph. 1.) 2.)](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649e7e5503460f94b8253f/html5/thumbnails/8.jpg)
Test the following equation Test the following equation for symmetry.for symmetry.
1.)1
42
2
x
xy
![Page 9: 2.2: Do Now: Determine if the following point is on the graph. 1.) 2.)](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649e7e5503460f94b8253f/html5/thumbnails/9.jpg)
Test the following equation Test the following equation for symmetry.for symmetry.
2.) xxy 3
![Page 10: 2.2: Do Now: Determine if the following point is on the graph. 1.) 2.)](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649e7e5503460f94b8253f/html5/thumbnails/10.jpg)
Test the following equation Test the following equation for symmetry.for symmetry.
3.) 2yx
![Page 11: 2.2: Do Now: Determine if the following point is on the graph. 1.) 2.)](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649e7e5503460f94b8253f/html5/thumbnails/11.jpg)
Test the following equation Test the following equation for symmetry.for symmetry.
4.)x
y1
![Page 12: 2.2: Do Now: Determine if the following point is on the graph. 1.) 2.)](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649e7e5503460f94b8253f/html5/thumbnails/12.jpg)
2.3 - Do Now: slope2.3 - Do Now: slopeFind the slope of the line passing through (1, 2) and (5, -3).
![Page 13: 2.2: Do Now: Determine if the following point is on the graph. 1.) 2.)](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649e7e5503460f94b8253f/html5/thumbnails/13.jpg)
Academy Algebra Academy Algebra IIII
2.3: LinesHW: p.185-186 (13, 22, 26,
29, 32, 40, 48, 53, 58, 90, 91)
![Page 14: 2.2: Do Now: Determine if the following point is on the graph. 1.) 2.)](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649e7e5503460f94b8253f/html5/thumbnails/14.jpg)
Draw a graph of the line that Draw a graph of the line that passes through the given point passes through the given point
with the given slope.with the given slope.
5
4);2,3( m
![Page 15: 2.2: Do Now: Determine if the following point is on the graph. 1.) 2.)](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649e7e5503460f94b8253f/html5/thumbnails/15.jpg)
Graph the equation.Graph the equation.1.) 2.)
3x 2y
![Page 16: 2.2: Do Now: Determine if the following point is on the graph. 1.) 2.)](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649e7e5503460f94b8253f/html5/thumbnails/16.jpg)
Graph the equation using Graph the equation using intercepts.intercepts.
3.) 842 yx
![Page 17: 2.2: Do Now: Determine if the following point is on the graph. 1.) 2.)](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649e7e5503460f94b8253f/html5/thumbnails/17.jpg)
Writing equations of lines.Writing equations of lines.Slope-intercept form:
Point-slope form:
Standard form:
![Page 18: 2.2: Do Now: Determine if the following point is on the graph. 1.) 2.)](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649e7e5503460f94b8253f/html5/thumbnails/18.jpg)
Find the slope and y-intercept Find the slope and y-intercept of the equation.of the equation.
2x + 4y = 8
![Page 19: 2.2: Do Now: Determine if the following point is on the graph. 1.) 2.)](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649e7e5503460f94b8253f/html5/thumbnails/19.jpg)
Write an equation of the Write an equation of the line with the following:line with the following:
1.) Slope = 2, y-intercept = 5.
2.) Passing through (1, 2), slope = 4.
![Page 20: 2.2: Do Now: Determine if the following point is on the graph. 1.) 2.)](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649e7e5503460f94b8253f/html5/thumbnails/20.jpg)
Write an equation of the Write an equation of the line with the following:line with the following:
3.) Horizontal line passing through (3, 2).
4.) Passing through (2, 3) and (-4, 5).
![Page 21: 2.2: Do Now: Determine if the following point is on the graph. 1.) 2.)](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649e7e5503460f94b8253f/html5/thumbnails/21.jpg)
Parallel and Perpendicular Parallel and Perpendicular LinesLines
• How do you know if lines are parallel?
• How do you know if lines are perpendicular?
![Page 22: 2.2: Do Now: Determine if the following point is on the graph. 1.) 2.)](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649e7e5503460f94b8253f/html5/thumbnails/22.jpg)
Parallel and Perpendicular Parallel and Perpendicular LinesLines
1.) Show that the lines are parallel:
2.) Show that the lines are perpendicular:
064:,632: 21 yxLyxL
62:,62: 21 xyLyxL
![Page 23: 2.2: Do Now: Determine if the following point is on the graph. 1.) 2.)](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649e7e5503460f94b8253f/html5/thumbnails/23.jpg)
Write an equation of the Write an equation of the line with the following:line with the following:
1.) Passes through (2, -3) and parallel to 2x + y = 6.
2.) Passes through (1, -2) and perpendicular to x + 3y = 6.