3.3 – The Equation of a Line

3.3 – The Equation of a Line

Slope-Intercept Form:

Point-Slope Form:

Standard Form:

Three Forms of an Equation of a Line

Note: A, B, and C cannot be fractions or decimals.

This form is useful for graphing, as the slope and the y-intercept are readily visible.

The point-slope form allows you to use ANY point, together with the slope, to form the equation of the line.

y mx b

m = slope of line b = y-intercept

62

5y x


Slope-Intercept Form– requires the y-intercept and the slope of the line.


y mx b


24

3y x


y mx b


33

2y x



y mx b


34

4y x



Write an equation of a line given the slope and the y-intercept.

9intercept = 2

11m y y

7intercept 5

3m y y

21 30,

13 4m

y

9

11x 2

7

3 x 5

21

13x

3

4

y mx b


Point-Slope Form – requires the coordinates of a point on the line and the slope of the line.

1 1y y m x x

11 2

3y x

2,11

3m



1 1y y m x x

32 3

4y x

3,2 3

4m



1 1y y m x x

44 2

5y x

2, 4 4

5m


Writing an Equation Given Two Points

Ax By C

1. Calculate the slope of the line.

2. Select the form of the equation.

a. Standard form

b. Slope-intercept form

c. Point-slope form

y mx b

1 1y y m x x

3. Substitute and/or solve for the selected form.



1,3 5, 2

3 2

1 5m

5

4

5

4

2 3

5 1m

5

4

5

4

or

Given the two ordered pairs, write the equation of the line using all three forms.

Calculate the slope.



1,3 5, 25

4m

1 1y y m x x

53 1

4y x 5

2 54

y x

Point-slope form



1,3 5, 25

4m

53 1

4y x 5

2 54

y x

5 53

4 4y x

5 53 3 3

4 4y x

5 17

4 4y x

5 252

4 4y x

5 252 2 2

4 4y x

5 17

4 4y x

Slope-intercept form y mx b



1,3 5, 2 5

4m

5 17

4 4y x

Standard form

LCD: 4

5 17

4 44 4 4y x

4 5 17y x

5 4 17x y


Solving Problems


Solving Problems

The pool Entertainment company learned that by pricing a pool toy at $10, local sales will reach 200 a week. Lowering the price to $9 will cause sales to rise to 250 a week.

a. Assume that the relationship between sales price and number of toys sold is linear. Write an equation that describes the relationship in slope-intercept form. Use ordered pairs of the form (sales price, number sold).

b. Predict the weekly sales of the toy if the price is $7.50.


Solving Problems

,sales price number sold

10,200 9,250

250 200

9 10m

50

1m

50m

200 50 10y x

200 50 500y x

50 700y x

250 50 9y x

250 50 450y x

50 700y x


Solving Problems

,sales price number sold

50 700y x 7.50x

Predict the weekly sales of the toy if the price is $7.50.

50 7.50 700y

375 700y

325y items sold


Are the ordered pairs a solution to the problem?

11

3y x

3, 2

1,3

yes

no

2 2

43

3

11

32 3

3 11

13

3.4 – Linear Inequalities in Two Variables

Are the ordered pairs a solution to the problem?

3, 2

1,3

3,0

4, 3

.


true

true

true

false

The shaded region represents the solution set for the inequality.

1, 4

2,2


Graph the solution set of the linear inequality

false

true

3 2 10x y

4,3

0,0

3 1

0 5

35

2y x



false

true

3y x

2,2

3,3

2 6

3 9



false

true

0,0

2, 3

01553 yx

35

3 xy

30

5

443



false

true

3.3 – The Equation of a Line

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