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1.1 POINTS AND LINES OBJECTIVES: FIND THE INTERSECTION OF TWO LINES, FIND THE LENGTH BETWEEN TWO POINTS, AND FIND THE MIDPOINT OF A SEGMENT Discrete Mathematics

Graphing (x, y) Quadrant I (+, +) Quadrant II (-, +) Quadrant III (-, -) Quadrant IV (+, -) Origin (0, 0)

Forms of Equations

Slope of a Line

Types of Slopes Positive Slope Increasing Line In the form y = mx + b

Types of Slopes Negative Slope Decreasing Line In the form y = mx + b

Types of Slopes Zero Slope Horizontal Line In the form y = #

Types of Slopes No Slope Vertical Line In the form x = #

Intersection of Lines

Distance

Midpoint

Formative Assessment Pg. 5-6 (1-7, 11, 15-21, 25) odd

Closing Question Pg. 5-6 (1-7, 11, 15-21, 25) odd Find the midpoint and distance between… (5,-1) and (8, 3)

Warm-up Find the distance and midpoint between (-3,4) and (3,-2)

Discrete Mathematics 1-2 SLOPES OF LINES OBJECTIVES: FIND THE SLOPE OF A LINE AND DETERMINE IF LINES ARE PARALLEL OR PERPENDICULAR

Slope

Slope-Intercept Form -7x

Parallel Lines When lines are parallel…..  The lines never intersect  The slopes are equal  Slope of line 1 = Slope of line 2 line 1 line 2

Perpendicular Lines line 1 line 2

Formative Assessment Homework #2

Formative Assessment Pg (1-19) odd What is the slope of the line in #7?

Find the slope for lines that go through the following points…. 1) (2,3) AND (4,5) 2) (0,0) AND (2,-5) 3) (-2,-2) AND (3,1)

Discrete Mathematics 1-3 FINDING EQUATIONS OF LINES OBJECTIVES: FIND AN EQUATION OF A LINE GIVEN CERTAIN PROPERTIES

Forms of Equations

Find the Equation of the Line

Perpendicular Bisector A line that intersects a segment at a right angle and it divides the segment into two equal parts. The slopes of perpendicular lines are opposite reciprocals. The line runs through the midpoint for a bisector.

Find the Equation of The Perpendicular Bisector

Formative Assessment Written Exercises Pg. 16 (1-15) odd

Formative Assessment

Please find an equation for a perpendicular bisector of the segment joining… (2,4) (4,-4) Warm-up! Happy Friday Everyone!

Please find f(3) and f(-8) if… f(x) = -3X -10 f(x) = 22X + 8 Warm-Up! Happy Monday!

Please write the equation for the… Distance formula Midpoint Slope Point-slope form Closing Question

Discrete Mathematics 1-4 LINEAR FUNCTIONS AND MODELS OBJECTIVES: MODEL REAL-WORLD SITUATIONS USING LINEAR FUNCTIONS

Independent Variable  Horizontal Axis  Determines the situation  Cannot Change Dependent Variable  Vertical Axis  Depends on the independent variable  Changes based on the situation Variables

Function Notation

Evaluating Functions

Constant Function  The slope is zero  Horizontal line  Example: h(t) = 3 Linear Function  The slope is + or –  Increasing or decreasing line  Example: L(T) = T + 10 Types of Functions

Domain  Set of values for which the function is defined  Independent Variable  Horizontal Axis Range  Set of dependent values  Vertical Axis Values of Functions

A Zero of a Function  When the function = 0  When y = 0  Where the graph crosses the independent axis  Can find using a calculator Example  Find the zeros of M(n) = 5n – 200 Values of Functions

Written Exercises Pg (1-15) odd Formative Assessment

On the calculator  2 nd Trace = Calculate Menu  #1: Value  #2: Zero  #5: Intersect Pg (1-15) odd Exit Clicker Question Join Code 13 Choose the best solution to #3 (A) Yes(B) No Formative Assessment