Warm-Up Writing Linear Equations - Edgenuity Inc.

Warm-Up Writing Linear Equations

?

Lesson

Question

Lesson Goals

Examine the different

of linear equations that

can be written given various pieces of information.

Write a linear equation

given two

.

Use two methods to write

the

-intercept

form of a line.

Model real-world functions

given various pieces of information.

W2K

Words to Know

Fill in this table as you work through the lesson. You may also use the glossary to

help you.

the form + = , where , and are real numbers such that and are not both zero, is positive if it is not zero, and the greatest common factor of , , and is 1

a linear relation written as - 1 = - 1 , where is the slope and (1, 1) is a point on the line

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Warm-Up Writing Linear Equations

W2K

Words to Know

a relationship between independent and dependent variables characterized by a constant rate of change, a highest degree of 1, and a graph that is a straight line

a linear relation written as = + , where and are real numbers, is the slope, and is the -intercept of the line

Forms of Linear Equations

The equation of a line can be written in different forms.

Slope-intercept form of a linear equation = +

= -5 +

Point-slope form of a linear equation - 1 = ( - 1)

1 - 4 = 3 + 4

(-5, )

Standard form of a linear equation

+ = 8 - 3 = 7

, Both 0 , , =

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Instruction Writing Linear Equations

Slide

2

Writing an Equation Given Two Points on the Line

Write the equation of the line that passes through the points (-2, -3) and (8, 3),

first in point-slope form, and then in slope-intercept form.

Find the slope: =

3 - -3 8 - -2

=

=

3 5

-

3 = 5 ( - 8)

- 3 = 3 + -24

5

5

+3

+ 15

5

= 3 +

5

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Instruction Writing Linear Equations

Slide

4

Writing the Standard Form of a Line

Write the equation of the line that passes through the points (-2, -3) and (8, 3) in

standard

form,

given

that

the

point-slope

form

is

-

3

=

3 5

(

-

8).

5 ( - 3) = 3 ( - 8) 5

5

5 - 15 =

5 - 15 = 3 - -3 + 15 - 3 + 15

-1 -3 + 5 = -9 -1

=9

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Instruction Writing Linear Equations

Slide

6

Comparing Different Equations That Represent the Same Line

The equation of the line that passes through the points (? 2, ? 3) and (8, 3) can be

written in different forms.

10 y

10 y

10 y

x

x

x

?10

10

?10

10

?10

10

?10

3 y?3= 5 x?8

point-slope form

Point: (8,

)

Slope:

3 5

?10

39 y= x?

55

slope-intercept form -intercept: -9 =

5

Slope: 3

5

?10

3x ? 5y = 9

form -intercept: 3 -intercept:

9 - 5 = -1.8

Writing a Linear Equation Given a Table

Write the equation of a line that passes through the points shown in the table.

- 1 = - 1

9-4 = 3 - 1 =

?5

?11

?1

?1

5

1

4

- 4 = 2 (

)

3

9

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