Download Chapter 1B

Chapter 1B (modified)
Give an explanation of the
midpoint formula and WHY
it works to find the
midpoint of a segment.
Quadrant II Quadrant I
(+,+)
(-,+)
Quadrant III Quadrant IV
(-,-)
(+,-)
Find the length of
AB, BD, and DE:
A
D
B
E
The distance between any two points with
coordinates (x1,y1) and (x2,y2) is given by
the formula:
Find the distance of LM is L(-6,4) and
M(2,3).
Find the distance of AB if A(-11,-1) and
B(2,5)
Find the midpoint of
AB, BD, and DE:
A
D
B
E
In a coordinate plane the coordinates
of the midpoint of a segment whose
endpoints have coordinates (x1,y1) and
(x2,y2) is given by the formula:
Find the coordinates of the midpoint
M of QS with endpoints Q(3,5) and
S(7,-9)
The midpoint of AB is M. If the coordinates of
M are (3,-4) and A(2,3) what are the
coordinates of B?
Homework: Lesson #1 – The
Coordinate Plane
(on Moodle)
Explain why a horizontal
line has a slope of 0, yet a
vertical line has a slope that
is undefined.
The ratio of the vertical change to the horizontal change
between any two points on a line.
Positive Slope
Rise
Run
Negative Slope
Zero Slope
Horizontal Line
Undefined Slope
Vertical Line
Find the slope of the line.
Rise
y2 – y1
=
Run
x2 – x1
Find the slope of the line that contains the
following points.
(-3,-4) and (5,-4)
(-2,2) and (4,-2)
(-3,3) and (-3,1)
(3,0) and (0,-5)
A linear equation in the form
y = mx + b
Slope y-intercept
Rise
Run
Where the
graph touches
the y-axis
x=0
Graph each equation
y = 3x – 4
y = -2x - 1
Write an equation for each line
The slopes of parallel lines are equal.
Vertical lines are parallel to one another.
Horizontal lines are parallel to one another.
Write an equation for each line
The slopes of
perpendicular lines are
opposite reciprocals of
one another.
Vertical Lines are
perpendicular to
horizontal lines.
Determine which lines are parallel and
which are perpendicular.
a)
b)
c)
d)
e)
y = 2x + 1
y = -x
y=x–4
y = 2x
y = -2x + 3
Determine if AB and CD are parallel,
perpendicular, or neither.
A(-3,2) B(5,1)
C(2,7) D(1,-1)
A(4.5,5) B(2,5)
C(1.5,-2) D(3,-2)
Homework: Lesson #2a –
Parallel and Perpendicular
Lines (on Moodle)
A linear equation in the form
(y – y1) = m(x – x1)
Slope
Point
Rise
Run
The coordinates
of any point on
the line
Example: m = 2 and the line passes through (4,3)
1. Put the slope and the coordinates of one
point in the point-slope form
2. Simplify to slope intercept form (y = mx + b)
Write an equation for a line with the given
slope and passes through the given point.
m = -3 and (5,8)
m = 2/3 and (6,9)
Example: A line passes through (9,-2) and (3,4)
1.
Calculate slope
2.
Put the slope and the coordinates of one point in
the point-slope form
3.
Simplify to slope intercept form (y = mx + b)
Write an equation for a line that passes
through the given points.
(1,2) and (3,8)
(8,-3) and (4,-4)
Homework: Lesson #2b - Glencoe Algebra
1 Practice Worksheet 4-2
(on Moodle)
Describe two ways to
determine which region of
the plane should be shaded
for linear inequalities.
An expression using >, <, ≥, or ≤.
y < 5x + 6
The solution is a region of the coordinate
plane, whose coordinate satisfy the given
inequality.
Determine if the following points are
solutions to the inequality:
y < 5x + 6
(4,26)
(-1,-5)
1. Solve the inequality for y
(slope-intercept form).
~~IF YOU MULTIPLY OR DIVIDE BY A
NEGATIVE FLIP THE SIGN~~
Graph the inequality:
-2x – 3y ≤ 3
2. Graph the equation.
•
EQUAL- a solid line. (≥,≤)
•
NOT EQUAL TO- a dotted line
(>, <)
Graph the inequality:
-2x – 3y ≤ 3
3. Shade the plane.
•
LESS THAN- Shade BELOW the
line. (<,≤)
•
GREATER THAN- Shade ABOVE
the line. (>,≥)
Graph the inequality:
-2x – 3y ≤ 3
Graph the inequality:
-2x – 3y ≤ 3
Graph the inequality:
y > 3x + 1
Graph the inequality:
2x + y < -2
Homework: Lesson #3 - Glencoe Algebra 1
Skills Practice 5-6 (on Moodle)