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Transcript of Chapter 1B (modified). Give an explanation of the midpoint formula and WHY it works to find the...
![Page 1: Chapter 1B (modified). Give an explanation of the midpoint formula and WHY it works to find the midpoint of a segment.](https://reader035.fdocuments.net/reader035/viewer/2022081516/5697bfa91a28abf838c99f3a/html5/thumbnails/1.jpg)
LINEAR EQUATIONS
Chapter 1B (modified)
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THE COORDINATE
PLANE
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Give an explanation of the midpoint formula and WHY it works to
find the midpoint of a segment.
ESSENTIAL QUESTION LESSON #1
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Quadrant I
(+,+)
Quadrant II
(-,+)
Quadrant IV
(+,-)
Quadrant III
(-,-)
THE COORDINATE PLANE
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A
B D
E
Find the length of AB, BD, and
DE:
THE COORDINATE PLANE
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The distance between any two points with coordinates (x1,y1) and
(x2,y2) is given by the formula:
DISTANCE FORMULA
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Find the distance of LM is L(-6,4) and M(2,3).
EXAMPLE 1
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Find the distance of AB if A(-11,-1) and B(2,5)
EXAMPLE 2
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A
B D
E
Find the midpoint of AB,
BD, and DE:
THE COORDINATE PLANE
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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
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Find the coordinates of the midpoint M of QS with
endpoints Q(3,5) and S(7,-9)
EXAMPLE 3
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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
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Homework: Lesson #1 – The Coordinate Plane
(on Moodle)
HOMEWORK
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PARALLEL AND PERPENDICULAR
LINES IN THE COORDINATE
PLANE
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Explain why a horizontal line has a
slope of 0, yet a vertical line has a
slope that is undefined.
ESSENTIAL QUESTION LESSON #2
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WHAT IS SLOPE?The ratio of the vertical change to the horizontal
change between any two points on a line.RiseRunPositive Slope Negative Slope
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WHAT IS SLOPE?
Zero SlopeHorizontal Line
Undefined SlopeVertical Line
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EXAMPLE 1Find the slope of the line.
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EQUATION FOR SLOPERise y2 – y1
Run x2 – x1
=
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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)
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SLOPE INTERCEPT FORMA linear equation in the formy = mx + b
SlopeRiseRun
y-interceptWhere the
graph touches the
y-axisx = 0
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EXAMPLE 3Graph each equation
y = 3x – 4 y = -2x - 1
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PARALLEL LINESWrite an equation for each line
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PARALLEL LINESThe slopes of parallel lines are equal.
Vertical lines are parallel to one another.
Horizontal lines are parallel to one another.
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PERPENDICULAR LINESWrite an equation for each line
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PERPENDICULAR LINES
The slopes of perpendicular lines
are opposite reciprocals of one
another.
Vertical Lines are perpendicular to horizontal lines.
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EXAMPLE 4Determine which lines are parallel
and which are perpendicular.
a) y = 2x + 1b) y = -xc) y = x – 4d) y = 2xe) y = -2x + 3
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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)
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Homework: Lesson #2a – Parallel and
Perpendicular Lines (on Moodle)
HOMEWORK
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WRITING LINEAR
EQUATIONS
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POINT-SLOPE FORMA linear equation in the form
(y – y1) = m(x – x1)
SlopeRiseRun
PointThe
coordinates of any point on the line
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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)
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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)
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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)
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EXAMPLE 7Write an equation for a line that passes
through the given points.(1,2) and (3,8) (8,-3) and (4,-4)
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Homework: Lesson #2b - Glencoe Algebra 1 Practice Worksheet 4-2
(on Moodle)
HOMEWORK
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LINEAR INEQUALITIE
S
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Describe two ways to determine which
region of the plane should be shaded for
linear inequalities.
ESSENTIAL QUESTION LESSON #3
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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.
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EXAMPLE 1Determine if the following points are
solutions to the inequality:
y < 5x + 6
(4,26) (-1,-5)
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GRAPHING INEQUALITIES1. Solve the inequality for y
(slope-intercept form).
~~IF YOU MULTIPLY OR DIVIDE BY A NEGATIVE FLIP THE SIGN~~
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EXAMPLE 2Graph the inequality:
-2x – 3y ≤ 3
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GRAPHING INEQUALITIES2. Graph the equation.
• EQUAL- a solid line. (≥,≤)
• NOT EQUAL TO- a dotted line (>, <)
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EXAMPLE 2Graph the inequality:
-2x – 3y ≤ 3
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GRAPHING INEQUALITIES3. Shade the plane.
• LESS THAN- Shade BELOW the line. (<,≤)
• GREATER THAN- Shade ABOVE the line. (>,≥)
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EXAMPLE 2Graph the inequality:
-2x – 3y ≤ 3
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ALTERNATE METHOD FOR SHADING.
Graph the inequality:-2x – 3y ≤ 3
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EXAMPLE 3Graph the inequality:
y > 3x + 1
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EXAMPLE 4Graph the inequality:
2x + y < -2
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Homework: Lesson #3 - Glencoe Algebra 1 Skills Practice 5-6 (on
Moodle)
HOMEWORK