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.