chapter 1b (modified). give an explanation of the midpoint formula and why it works to find the...

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