NOTES: SOLVING LINEAR EQUATIONS DAY 1

[Pages:33]NOTES: SOLVING LINEAR EQUATIONS

DAY 1

What are the steps to solving a linear equation?

1. ______________________________________________________

2. ______________________________________________________

3. ______________________________________________________

4. ______________________________________________________

5. ______________________________________________________

Practice: Solve for x without using a calculator.

1. x + (2x - 4) = 11

2.

x + ( x - 1) = 3x ? 1

3. x = ? (2 + 2x) ? x

4. (x - 2) + (2x + 4) = x

5. x = x + 2

6. x + (2x - 1) = 3x ? 1

TYPES OF SOLUTIONS

No Solution:

__________________________________________________________

All real numbers: _____________________________________________________

One Solution:

For each equation, classify the equation as No Solution, All Real Number Solutions, or One Solution.

7. x + 2 = x + 3

8. 2x = 3x

9. 2x + 8 = 6 ? x

10. 2x - 4 + 3x = 8x ? 5

11. 2x + 5 = 5 + 2x

12. (x + 3) - (x - 3) = 3

NOTES: FUNCTION DEFINITION

DAY 2

I. Vocabulary

Domain: The set (

) of all inputs (x-values) of a function.

Range:

The set (

) of all outputs (y-values) of a function.

Relation: Every two sets has some kind of relationship. That relationship is called a relation.

Function ? A function is a type of relation that has the following property: Every element of the domain is paired up with exactly one element of the range. (for every input there is one and only one output!)

How do we find the domain and range of a function?

1. Analytically ? find reasonable values for the independent variable and will produce reasonable values for the dependent variable.

2. Look at a graph. Domain: smoosh the graph onto the x-axis to find all the x-values Range: smoosh the graph onto the y-axis to find all the y-values

3. Use a table of ordered pairs.

1.

2.

3.

Domain: __________________ Domain: __________________ Domain: __________________ Range:____________________ Range:____________________ Range:____________________

NOTES: RULE OF FOUR

DAY 2

Below are four ways to represent relations. Determine if the relation is a function or not and explain.

1. Mapping Diagram

Is f a function or not? ________________ Why?

2. Table

Input (x) -4 -2 0 1 5 7

Output (y) -1 3 -5 -1 0 0

Is g a function or not? ________________ Why?

2. Ordered Pairs Diagram h: {(-3, 5), (0, 8), (2, -3), (6,-4), (8, 5)} Is h a function or not? ________________ Why?

i: {(-7, 6), (-4, 2), (-4, -5), (1,3), (2, 6)} Is i a function or not? ________________ Why?

4. Graph Is l a function or not? Why?

Repeating

Vertical Line Test

NOTES: EQUATION OF A LINE

DAY 4

Vocabulary:

y = mx+b

Slope (m):______________________________________________________________ y-intercept (b):_________________________________________________________

Practice: Identify the slope and y-intercept of each equation.

1)

slope: _____________

y-intercept ( ___,___)

2)

slope: _____________

y-intercept ( ___,___)

3)

slope: _____________

y-intercept ( ___,___)

4)

slope: _____________

y-intercept ( ___,___)

5)

slope: _____________

y-intercept ( ___,___)

Practice: Identify whether the graph of the equation will be linear growth or linear decay.

1)

linear growth/linear decay

2)

linear growth/linear decay

3)

linear growth/linear decay

4)

linear growth/linear decay

PRACTICE:Circlealllinearfunctions.

1. y=6x+4

2. y=-2(x+3)+10

3. 3x?5=y?4x+6

4. y=6

5. x=6

NOTES: GRAPHING LINEAR FUNCTIONS

DAY 4

Guitar Lessons. Mrs. Ausel is interested in finding guitar lessons. A local music studio has told him that for 6 hours of instruction the cost will be $159. For 10 hours of instruction the cost will be $255. Let x represent the number of instructional hours and y represent the cumulative cost ($).

Write an equation of a line to represent how much he will pay, y, for the number of hours of guitar lessons, x. Hint: write the given information as two ordered pairs.

Y=mx+b

Look at each graph. Find the slope of the line (m) by counting rise and run. Find the y intercept (b). Use this information to write the equation of the line.

1. EQUATION:

Slope =

Y intercept =

2.

EQUATION:

Slope =

Y intercept =

3.

EQUATION:

Slope =

Y intercept =

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