the following point is on the following point is on the graph. the graph. 1.) 2.) ) 2 , 2 ( ; 6 2 y x ) 4 , 1 ( ; 1 3 2 y x
Dec 29, 2015
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
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)
Graph the equation. Graph the equation. (By hand & on calculator.)(By hand & on calculator.)
1.) 2.) 52 xy 2xy
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
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.
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.
Academy Algebra Academy Algebra IIII
2.2: FinishHW: p.172 (56, 59, 61, 68)
Test the following equation Test the following equation for symmetry.for symmetry.
1.)1
42
2
x
xy
Test the following equation Test the following equation for symmetry.for symmetry.
2.) xxy 3
Test the following equation Test the following equation for symmetry.for symmetry.
3.) 2yx
Test the following equation Test the following equation for symmetry.for symmetry.
4.)x
y1
2.3 - Do Now: slope2.3 - Do Now: slopeFind the slope of the line passing through (1, 2) and (5, -3).
Academy Algebra Academy Algebra IIII
2.3: LinesHW: p.185-186 (13, 22, 26,
29, 32, 40, 48, 53, 58, 90, 91)
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
Graph the equation.Graph the equation.1.) 2.)
3x 2y
Graph the equation using Graph the equation using intercepts.intercepts.
3.) 842 yx
Writing equations of lines.Writing equations of lines.Slope-intercept form:
Point-slope form:
Standard form:
Find the slope and y-intercept Find the slope and y-intercept of the equation.of the equation.
2x + 4y = 8
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.
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).
Parallel and Perpendicular Parallel and Perpendicular LinesLines
• How do you know if lines are parallel?
• How do you know if lines are perpendicular?
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
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.