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