Chapter 1.1 Lines

Objectives Increments Slope Parallel and Perpendicular Equations Applications

Learning Target 80% of the students will be able to find the equation of a line, given two points on the line.

Standard G-GPE.5Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

Calculus Calculus was invented to help physicists understand motion. Calculus relates rate of change of a quantity to a graph of the quantity. Explaining that relationship is the goal of this course. We will start by examining slopes.

Increments Particle in motion: Changes in position are increments. Subtract the coordinates of its starting point from the coordinates of its ending point.

Definition

Example 1: Finding Increments

Exercise 1

Slope of a Line

Parallel Lines  11

Perpendicular Lines

Vertical Lines

Horizontal Lines

Exercise 2

Point-Slope Form

Exercise 3

Slope-Intercept Form

X -Intercept The x  coordinate of the point where a nonhorizontal line crosses the x  axis is the x  intercept.

Exercise 4

General Form

Graphing a General Linear Equation

To use a graphing Calculator, Transform the linear equation from general form to slope-intercept form Enter it into the equation editor of the graphing calculator

Exercise 5

Writing Equations

Exercise 6

Determining Linear Functions

Exercise 7 Find the linear function that produced the following table: x f(x)f(x)

Conversions

Exercise 8

Regression Analysis

Regression Analysis – Example Enter the data Generate a scatter plot Perform the regression analysis

Regression Analysis – Continued Graph the regression curve Predict the population for 2010

Homework Page 9: 1-21 every other odd (EOO, 1,5,9,etc.), 22, 23, 25-37odds, all, 43, 44, all, 54, 55, 57