2 – 4: Writing Expressions2 – 4: Writing Expressionsof Lines of Lines (Day 1(Day 1 ) )

Objective:

CA Standard 1: Students solve equations and inequalities involving absolute value.

Writing Linear Writing Linear EquationsEquations

Slope - Intercept Form: Given the slope m and the y-intercept b, use this equation

y mx b

Point – Slope Form: Given the slope m and a point (x1, y1), use this equation:

1 1y y m x x

Two Points: Given two point (x1, y1), and (x2,

y2), use the formula

2 1

2 1

y ym

x x

to find the slope m.

Example 1: Writing an Example 1: Writing an Equation Given the slope Equation Given the slope

and y-intercept.and y-intercept. 4

2

-2

-5 5

2

3

(0,-1)

From the graph of the line determine the slope.

m = 3/2

What is the y-intercept?

(0, -1)

What is an equation of this line?

y = mx +b

y = 3/2 x – 1

Example 2Example 2 Write an equation of the line that passes through (2, 3) and has a slope of – ½ .

Use the point – slope form

1 1y y m x x

13 2

2y x

3 12

xy

42

xy

Example 3Example 3

Write an equation of a line that passes through (3, 2) and is parallel to the line

y = -3x +2.

If two lines are parallel they have the same slope.

Let m = -3 and (x1, y1) = (3, -2)

2 3 3y x

2 3 9y x

3 11y x

Use the point slope form.

2 3 3y x

Write an equation of a line that passes through (3, 2) and is perpendicular to the line

y = -3x +2.

If two lines are perpendicular then the product of their slopes is –1.

Example 4Example 4

Use the point slope form find the equation of the line

1 1y y m x x

12 33

y x

2 13

xy

13

xy

Let m1 = -3

m1 m 2 = -1

-3 m2 = - 1

m2 = -1/-3

m2 = 1/3

Example Example 5:5:

Write an equation of a line that passes through

(-2, -1) and (3, 4)

Find the slope:

2 1

2 1

4 1

3 2

y ym

x x

51

5

Use the point slope form.

1 1y y m x x

1 1 2y x

1 2y x

1 2y x

Example 6: Writing and Example 6: Writing and using a Linear Model.using a Linear Model.

In 1984 Americans purchased an average of 113 meals or snacks per person at

restaurants. By 1996 this number was 131. Write a linear model for the number of meals

or snacks purchased per person annually.

Then use the model to predict the number of meals that will be purchased per person in

2006.

Average rate of change

131 113

1996 1984

18 31.5

12 2

Verbal Model:

Labels

Number of Meal y

Number in 1984 113

Average Rate of change 1.5

Year since 1984 t = 2006 –1984

t = 22

y = 113 + 1.5 t

y = 113 + 1.5 (22)

y = 113 + 33

y = 146

Algebraic Model

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