Sec 3.7 Equations of Lines in the Coordinate Plane Chapter 3.

Sec 3.7 Equations of Lines in the Coordinate Plane Chapter 3

Review

If two lines are cut by a transversal they form special properties. Corresponding angles Alternate interior angles Alternate exterior

angles Are congruent.

Are parallel

Same-side interior angles are supplementary.

Two lines to the same line are to each other.

In a plane, two lines to the same line are .

Lesson Purpose

Objective

Write an equation of a line given characteristics of parallel or perpendicular lines.

Essential Question

How can you prove that two lines are parallel?

What is a slope?

The steepness of a hill

A positive(+) slope:

If you go from left to right and you go up, it is a positive slope

Different types of slopesA negative(-) slope:

If you go from left to right and you go down, it is a negative slope

A zero (0) slope:

If you go from left to right and you don't go up or down, it is a zero slope

No Slope orSlope UndefinedVertical lines have no slope, or undefined slope.

Ski Bird cannot ski vertically.  Sheer doom awaits Ski Bird at the bottom of a vertical hill.

A slope of a line contains two points (x₁, y₁) and (x₂ ,y₂).

Slope Equation

Example #1 Let’s find the slope of

the line passing through the given points.

(2,3),(-1,-6)

Step 1: use slope equation:

Step 2: set up equation with points given:

Step 3: solve

What kind of slope is it?

Question #1

What is the slope of the line passing through the points (2, 7) and (21, 3)?

A. 2/7 B. 3/4 C. 4/3 D. 1/3

Question #2 What is the slope of the line passing

through the points (-2,-3) and (1, 3)?

A. 1/2 B. 2 C. -2 D. -1/2

Example #2 What is the slope

of the line?

Question #3 Find the slope of the

line?

A. 1/4 B. -1/4 C. -4 D. 4

Question #4 Find the slope of

the line? A. 2/3 B. 3/2 C. -2/3 D. -3/2

Parallel lines have the same slope.

3.8 Slopes of Parallel lines

The product of the slopes of two perpendicular lines is -1 or the slopes are negative reciprocal. Product means multiplication.

Slopes of Perpendicular Lines

Slope-Intercept Form -is an equation of a

non-vertical line is y=mx+b where m is the slope

and b is y-intercept

Example #3 Graph the equation of the line

y= ½x+2 Step 1: identify the slope

and y-intercept

Step 2 : plot your y- intercept

Step 3: connect the points

Question #5 Graph the equation y= ½x-3

A. B

D.C.

Question #6 Graph the equation y= -2x-2

A B

C D

Real World Connections

Ticket Out and Homework Is it always necessary

to identify both the slope and y-intercept of a line when graphing its equation? Explain

pg. 207-208 #’s 5, 6, 7,9,10, 14, 15, 18,19,20,21