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Hands-on Activity: Competition Time Matching : Slope-Intercept Form & Graph

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Page 1: Hands-on Activity: Competition Time Matching: Slope-Intercept Form & GraphMatching: Slope-Intercept Form & Graph

Hands-on Activity: Competition Time

• Matching: Slope-Intercept Form & Graph

Page 2: Hands-on Activity: Competition Time Matching: Slope-Intercept Form & GraphMatching: Slope-Intercept Form & Graph

Home-Learning Assignment #3 - Home-Learning Assignment #3 - ReviewReview

Page 3: Hands-on Activity: Competition Time Matching: Slope-Intercept Form & GraphMatching: Slope-Intercept Form & Graph

What we Know so far….What we Know so far….

Slope Intercept Form

bmxy

Where m is the slope and b is the intercept

Name:Date: Period:

Quick Review:

Topic: 1. Point-Slope Form 2. Standard FormEssential Question: What can be used to write and graph the equation of a line? Which form would better help me graph & write linear equations?

Page 4: Hands-on Activity: Competition Time Matching: Slope-Intercept Form & GraphMatching: Slope-Intercept Form & Graph

By the end of today’s class you will be able to write and graphlinear equations using point-slope form

By the end of today’s class you will be able to write and graphlinear equations using point-slope form

Objective:

In this lesson you will learn a different strategy – one

that uses the point-slope form of an equation of a line

Previously you learned one strategy for writing a linear equation

when given the slope and a point on the line..

Page 5: Hands-on Activity: Competition Time Matching: Slope-Intercept Form & GraphMatching: Slope-Intercept Form & Graph

The New Stuff… Point- Slope The New Stuff… Point- Slope FormFormPoint- Slope form is:

)( 11 xxmyy Where m is the slope

and (x1,y1) is the given point

Page 6: Hands-on Activity: Competition Time Matching: Slope-Intercept Form & GraphMatching: Slope-Intercept Form & Graph

Example #1

Write the equation of the line that goes through the point (2, –3) and has a slope of 4.

Point = (2, –3)

Slope = 4

y – y1 = m (x – x1)

y + 3 = 4 (x – 2)

Starting with the point – slope form

Plug in the y-value, the slope, and the x-value to get

Notice, that when you replaced the “y1” it became “+3”.

Page 7: Hands-on Activity: Competition Time Matching: Slope-Intercept Form & GraphMatching: Slope-Intercept Form & Graph

Write the Equation in Point-Slope Write the Equation in Point-Slope FormForm

)6,1(3

1 andm

)( 11 xxmyy Step 1: Plug it in

Page 8: Hands-on Activity: Competition Time Matching: Slope-Intercept Form & GraphMatching: Slope-Intercept Form & Graph

1 2 43

5

-1-2-3-4-5

1

2

3

4

5-1

-2-3

-4

-5

What is the graph of y – 1 = (x – 2)?

Page 9: Hands-on Activity: Competition Time Matching: Slope-Intercept Form & GraphMatching: Slope-Intercept Form & Graph

??????

Using two points to write Using two points to write an equation in point-slope an equation in point-slope

formformCan you write the equation of a line in point-slope

form that passes through (-3,6) and (1,-2)

Page 10: Hands-on Activity: Competition Time Matching: Slope-Intercept Form & GraphMatching: Slope-Intercept Form & Graph

??????

Using two points to write an Using two points to write an equation in point-slope equation in point-slope

formform

1 2 43

5

-1-2-3-4-5

1234

5-1-2-3-4-5

(2,2)

(0,-3)

Page 11: Hands-on Activity: Competition Time Matching: Slope-Intercept Form & GraphMatching: Slope-Intercept Form & Graph

Standard Form

Ax + By = C

Page 12: Hands-on Activity: Competition Time Matching: Slope-Intercept Form & GraphMatching: Slope-Intercept Form & Graph

x-interceptx-intercept - the point (ordered pair) where a line crosses the x-axis.

y-intercepty-intercept - the point (ordered pair) where a line crosses the y-axis.

The word “intercept” means to cross.

Page 13: Hands-on Activity: Competition Time Matching: Slope-Intercept Form & GraphMatching: Slope-Intercept Form & Graph

Using Standard Form:To find an intercept, set the other

variable equal to zero.

3x – 5y = 15

Ax + By = C

Page 14: Hands-on Activity: Competition Time Matching: Slope-Intercept Form & GraphMatching: Slope-Intercept Form & Graph

1) 3x + 4y = 24

2) 7x + 8y = 21

Your Turn (Find x & y-intercept):

Page 15: Hands-on Activity: Competition Time Matching: Slope-Intercept Form & GraphMatching: Slope-Intercept Form & Graph

Graph using X & Y-intercepts:

1) 3x + 4y = 24

2) 7x + 8y = 21

Page 16: Hands-on Activity: Competition Time Matching: Slope-Intercept Form & GraphMatching: Slope-Intercept Form & Graph

Graphing Horizontal Lines: Slope is zero. Equation form is y = #.

a) y = -2

b) y = 3

c) y = 1

Page 17: Hands-on Activity: Competition Time Matching: Slope-Intercept Form & GraphMatching: Slope-Intercept Form & Graph

Graphing Vertical Lines: Slope is undefined. Equation form is x = #.

a) x = -1

b) x = 3

c) x = 4

Page 18: Hands-on Activity: Competition Time Matching: Slope-Intercept Form & GraphMatching: Slope-Intercept Form & Graph

Transforming to Standard Form (Ax + By = C):

y = 3x + 4

y = 3/7x + 4

y – 2 = - 1/3(x + 6)

Page 19: Hands-on Activity: Competition Time Matching: Slope-Intercept Form & GraphMatching: Slope-Intercept Form & Graph

Making the connection:

How can I write the following point-slope form in slope-intercept form?

y + 3 = 4 (x – 2)

How can I write the following standard form in slope-intercept form?

-4x + y = - 11

Page 20: Hands-on Activity: Competition Time Matching: Slope-Intercept Form & GraphMatching: Slope-Intercept Form & Graph

Practice:Practice:

Page 316-318Page 316-318

(2-6, 12, 35) (2-6, 12, 35)

Page 323 (6)Page 323 (6)

Page 21: Hands-on Activity: Competition Time Matching: Slope-Intercept Form & GraphMatching: Slope-Intercept Form & Graph

Review for Exam #4

Page 22: Hands-on Activity: Competition Time Matching: Slope-Intercept Form & GraphMatching: Slope-Intercept Form & Graph

Wrap-Up:Wrap-Up:

•Vocabulary & Forms Review

HLA #4: Point-Slope Form & Standard FormPage 316 – 318 (14, 16, 39)

Page 324 (12, 14)