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2-3:Linear Functions & Slope-Intercept Form

Mr. Gallo

Algebra 2

Linear Function

A function whose graph is a ________. A solution to a linear function is any

____________ that makes the equation true.

line

ordered pair

6 4f x x

Slope The ratio of the vertical change to the horizontal

change◦ The steepness or rate of change of a line

vertical change

horizontal change

change in y risem

change in x run 2 1

2 1

y y

x x

2

Slope-Intercept Form An equation written in the form: y mx b What is the equation of the line:

21

3y x

2

3m 1b

12 10 3y x

3 12 10x y 3 12

10 10x y

3 6

10 5x y

2-4: More About Linear EquationsMr. GalloAlgebra 2

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Finding a Linear Equation:

I. Given a Point and the Slope:

Find an equation of a line that passes through thepoint ( 7, 1) and has the slope 2/3

Use the point-slope form:

1) Substitute the slope and the values for x and y from the given point.

2

31 7y x

1 1my xy x

2 141

3 3y x

2 141

3 3y x

14 14 31

3 3 311

3

2 11

3 3y x

Point-Slope Form Slope-Intercept

II. Given Two Points:Find an equation of a line that passes

through the points (-3, 6) and ( 5, 0)

Use the point-slope form:

1) Find the slope:

2) Substitute the slope and one of the points into the equation.

2 1

2 1

y ym

x x

6 0

3 5

6

8

3

4

1 1y y m x x

30 5

4y x

3 150

4 4y x

3 15

4 4y x

4

Suppose you know that the formula relating blood pressure and age is linear and that normal systolic blood pressures are 110 for a 20-year-old and 130 for a 60-year-old. Construct a formula in which blood pressure B is a function of age A.

Example

20,110 60,130

2 1

2 1

y ym

x x

130 110

60 20

20

40

1130 60

2y x

1

2

1130 30

2y x

Return to the equation you wrote to relate systolic blood pressure and age:

1130 30

2y x

What graph models the situation?

20,110 60,130

140

120

100

80

60

40

20

20 40 60

Age

Write the equation in Slope-Intercept Form.

301

1002

y

1130 30

2y x

If someone is 30 yrs. old, what is their systolic blood pressure expected to be?

15 100 115

1100

2y x

5

Standard Form of a Linear Equation

The Standard Form of a linear equation is:

where A, B and C are real numbers and A and B are bothnot 0

A is the coefficient of xB is the coefficient of yC is a constant

Ax CBy

5

What is an equation of the line in standard form? Use

integer coefficients.

23

5y x

23

5y x

2 2

5 5x x

23

5x y

2 5 15x y

2Subtract from each side

5x

Get both variables on the same side.

Multiply term by the LCDevery

Complete Got It? #3 p. 83. Use Integer coefficients.

91 10 36x y

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Summary of Equation Forms

Writing Equations of Lines

y mx b 1 1y y m x x Ax By C

Slope-Intercept Form

Point-Slope Form

Standard Form

Use this form when you know the slope and the y-intercept.

Use this form when you know the slope and a point, or when you know two points.

A, B and C are real numbers.

A and B cannot both be 0.

Graph the equation 10x + 6y = 30 by using its intercepts:

To find the x-intercept substitute 0 for y

x-intercept:

To find the y-intercept substitute 0 for x

y-intercept:

Example:

(3, 0)

(0, 5)

7

What is the equation of each line in slope-intercept form?

1. The line parallel to through (-2,1).

2. The line perpendicular to with the same y-intercept as .

5 4y x

32

4y x

3 12x y

1 1y y m x x 5m

1 5 2y x

1 5 10y x

5 11y x

0 3 12y

3 12y

4y

1

2m 1

42

y x

Complete Got It? #6 p. 85. 36

2y x 2 6y x a). b).

Homework: p.78 #8, 9, 17, 20, 22, 24, 63-65, 67p. 86 #17, 21-25 odd, 31-33, 57-59