chapter 1b (modified). give an explanation of the midpoint formula and why it works to find the...
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LINEAR EQUATIONS
Chapter 1B (modified)
THE COORDINATE
PLANE
Give an explanation of the midpoint formula and WHY it works to
find the midpoint of a segment.
ESSENTIAL QUESTION LESSON #1
Quadrant I
(+,+)
Quadrant II
(-,+)
Quadrant IV
(+,-)
Quadrant III
(-,-)
THE COORDINATE PLANE
A
B D
E
Find the length of AB, BD, and
DE:
THE COORDINATE PLANE
The distance between any two points with coordinates (x1,y1) and
(x2,y2) is given by the formula:
DISTANCE FORMULA
Find the distance of LM is L(-6,4) and M(2,3).
EXAMPLE 1
Find the distance of AB if A(-11,-1) and B(2,5)
EXAMPLE 2
A
B D
E
Find the midpoint of AB,
BD, and DE:
THE COORDINATE PLANE
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:
MIDPOINT FORMULA
Find the coordinates of the midpoint M of QS with
endpoints Q(3,5) and S(7,-9)
EXAMPLE 3
The midpoint of AB is M. If the coordinates of M are (3,-4) and A(2,3)
what are the coordinates of B?
EXAMPLE 4
Homework: Lesson #1 – The Coordinate Plane
(on Moodle)
HOMEWORK
PARALLEL AND PERPENDICULAR
LINES IN THE COORDINATE
PLANE
Explain why a horizontal line has a
slope of 0, yet a vertical line has a
slope that is undefined.
ESSENTIAL QUESTION LESSON #2
WHAT IS SLOPE?The ratio of the vertical change to the horizontal
change between any two points on a line.RiseRunPositive Slope Negative Slope
WHAT IS SLOPE?
Zero SlopeHorizontal Line
Undefined SlopeVertical Line
EXAMPLE 1Find the slope of the line.
EQUATION FOR SLOPERise y2 – y1
Run x2 – x1
=
EXAMPLE 2Find 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)
SLOPE INTERCEPT FORMA linear equation in the formy = mx + b
SlopeRiseRun
y-interceptWhere the
graph touches the
y-axisx = 0
EXAMPLE 3Graph each equation
y = 3x – 4 y = -2x - 1
PARALLEL LINESWrite an equation for each line
PARALLEL LINESThe slopes of parallel lines are equal.
Vertical lines are parallel to one another.
Horizontal lines are parallel to one another.
PERPENDICULAR LINESWrite an equation for each line
PERPENDICULAR LINES
The slopes of perpendicular lines
are opposite reciprocals of one
another.
Vertical Lines are perpendicular to horizontal lines.
EXAMPLE 4Determine which lines are parallel
and which are perpendicular.
a) y = 2x + 1b) y = -xc) y = x – 4d) y = 2xe) y = -2x + 3
EXAMPLE 5Determine if AB and CD are
parallel, perpendicular, or neither.A(-3,2) B(5,1) A(4.5,5) B(2,5)
C(2,7) D(1,-1) C(1.5,-2) D(3,-2)
Homework: Lesson #2a – Parallel and
Perpendicular Lines (on Moodle)
HOMEWORK
WRITING LINEAR
EQUATIONS
POINT-SLOPE FORMA linear equation in the form
(y – y1) = m(x – x1)
SlopeRiseRun
PointThe
coordinates of any point on the line
GIVEN A SLOPE AND POINTExample: 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)
EXAMPLE 6Write 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)
GIVEN TWO POINTSExample: 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)
EXAMPLE 7Write 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)
HOMEWORK
LINEAR INEQUALITIE
S
Describe two ways to determine which
region of the plane should be shaded for
linear inequalities.
ESSENTIAL QUESTION LESSON #3
WHAT IS AN INEQUALITY?An expression using >, <, ≥, or ≤.
y < 5x + 6
The solution is a region of the coordinate plane, whose coordinate
satisfy the given inequality.
EXAMPLE 1Determine if the following points are
solutions to the inequality:
y < 5x + 6
(4,26) (-1,-5)
GRAPHING INEQUALITIES1. Solve the inequality for y
(slope-intercept form).
~~IF YOU MULTIPLY OR DIVIDE BY A NEGATIVE FLIP THE SIGN~~
EXAMPLE 2Graph the inequality:
-2x – 3y ≤ 3
GRAPHING INEQUALITIES2. Graph the equation.
• EQUAL- a solid line. (≥,≤)
• NOT EQUAL TO- a dotted line (>, <)
EXAMPLE 2Graph the inequality:
-2x – 3y ≤ 3
GRAPHING INEQUALITIES3. Shade the plane.
• LESS THAN- Shade BELOW the line. (<,≤)
• GREATER THAN- Shade ABOVE the line. (>,≥)
EXAMPLE 2Graph the inequality:
-2x – 3y ≤ 3
ALTERNATE METHOD FOR SHADING.
Graph the inequality:-2x – 3y ≤ 3
EXAMPLE 3Graph the inequality:
y > 3x + 1
EXAMPLE 4Graph the inequality:
2x + y < -2
Homework: Lesson #3 - Glencoe Algebra 1 Skills Practice 5-6 (on
Moodle)
HOMEWORK