Ring Notes For

Formal Relationships

Section [1.9]

Review Slope Intercept Form y = mx + b; Where “m” is the slope & “b” is y-intercept. Ex. m = 2 (0, -3); Substitute into y = mx + b So, y = 2x – 3 and you are Done! You Try: 1. (0, 1) m =

1 2

2. m = 0 and b = .5

3.

Δy Δx

=

2 3

(0, -4)

More equations… Point – Slope Form

y − y1 = m ( x − x1 ) When is it good to use this form? Answer in your own words: ______________________________________________ ______________________________________________

It is good to use the Point-Slope Form of Linear Equations, when you know the slope and one point on the line, or if you know any two points on the line.

Example: (1, 2) and (-5, 7);

Positioning Is Everything… …for example, use points (1, 2) and (-5, 7) to write equation. Let’s use…3CPC: Independent Process Dependent x

y

(x1)

1

(y1)

2

(x2)

-5

(y2)

7

x3

y3

x4

y4

1. To find the slope m = Δy = 5 . Δx

−6

Independent

-5 – 1 = -6

Process

Dependent

x

y

1

2

-5

7

7–2=5

2. Now use the Point Slope Form to write the equation.

y − y1 = m( x − x1 )

y – __ =

5 −6

(x – __); Distributive Prop.

Remember: (1, 2) is (x1, y1) (-5, 7) is (x2, y2) and m =

5 −6

y – 2 = ___x + ___; Add 2 to both sides. +2

y=

+2 5 −6

x+

17 6

;

Slope Intercept Form of a Linear Equation

Real World Application: A slow steady stream of water flows into a partially-filled rectangular tub. After 6 minutes, there are 26 gallons of water in the tub. After 17 minutes, there are 48 gallons. A. Write an equation to represent the volume of water in the tub y after x minutes.

B. How much water was in the tub to begin?

C. How long will it take to fill the tub to 60 gallons?

Solving Proportional Equations Predicting values from a proportional relationship (two fractions that are equal to each other) can be done by solving for the variable. Cross Example: 12 5 (11) 12

5

=

12 5

=

Multiplication or Cross Product is the most common way of solving for the variable.

y 11

y Multiply both sides by 11. 11

Then simplify the fraction for answer.

=

132 =y 5

y (11) 11 or

y = 26.4 You Try:

4 x

=

15 23