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Algebra 1B Assignments Chapter 6: Linear Equations

(All graphs must be drawn on GRAPH PAPER!) Review Worksheet: Rational Numbers and Distributive Property Review Worksheet: Solving Equations Quiz Rational Numbers, Distributive Property, Solving Equations 6-1 Pages 312-314: #1, 4, 7-9, 10-20 even, 22-27, 38-40, 43, 49, 51, 54-60, 62 6-5 Pages 339-341: #1-9, 11-17 odd, 19-29 odd (not slope-intercept form), 36-38, 56-60 even 6-2 Pages 320-322: #2, 3, 14, 15, 22-28, 33, 34, 38, 66-68 6-4 Page 333: #1-4, 15-20, 23, 24, 27, 30, 31 Quiz 6-1, 6-5, 6-2, 6-4 Review Worksheet: Slope-Intercept and Standard Form 6-8 Pages 361-362: #1, 2, 4, 5, 10, 11, 17, 18, 23, 26, 36-40

Worksheet: Absolute Value Review Worksheet: Chapter 6 Review Test Chapter 6: Linear Equations

Worksheet: Graphing Lines

Solving Equations

Objective: To review solving multi-step equations To solve an equation: Find value of a variable that makes the equation true

• use inverse operations (operations that undo each other – use reverse PEMDAS) • keep equation balanced (do the same thing to both sides) • check by plugging solution into original equation

Example #1 Solve the following equations. Check your answers.

a) 2( 4) 12x− − = b) 2 5 133

y + =

Example #2 Solve the following equations. Check your answers. a) 5 3 2 12m m− = + b) 6 (2 9) 8g g− − = Example #3 Solve the following equations. Check your answers.

a) 33 4c

= b) 4 25 7

e e+ −=

Example #4 Solve the following equations. Check your answers.

a) 2 1 73 2

a a + = b) 4(2 3) 5( 6) 3x x x− = + −

Example #5 Solve the following equations. Check your answers. a) 13 6 5 10 7v v v− − = + − b) 7 8 2(4 3) 1y y− = − − +

* no solution: no value of the variable will make the equation true (all variables cancel, left with “NOT TRUE”)

* identity: all values of the variable will make the equation true (all variables cancel, left with “TRUE”)

Example #6 You work for a delivery service. With Plan A you earn $5.00 per hour plus $0.75 per delivery. With Plan B you earn $7.00 per hour plus $0.25 per delivery. How many deliveries must you make per hour with Plan A to make as much money as Plan B? Closure Question What order of operations should you use to solve multi-step equations?

Section 6-1

Warm – Up: Write in simplest form.

1. 7 33 1

−−

2. 3 56 0

−− 3.

8 ( 4)3 7− −

−

4. 1 20 5

− −−

5. 0 11 0

−−

6. 7 ( 5)2 6

− − −− −

Objective: To find rates of change from tables and graphs, and to find slope

In the graph above, AB and BC have different rates of change vertical change

horizontal change

Example #1 For the data below, is the rate of change for each pair of consecutive days the same? What does the rate of change represent?

Example #2 Find the rate of change of the data in the graph.

* 2 1

2 1

vertical change riseslope rate of changehorizontal change run

y yx x

= = = =

−−

Example #3 Find the slope of each line. a) b) Example #4 Find the slope of the line through each pair of points. a) (3, 2) and (5, 10) b) (-1, 4) and (3, -2) Example #5 Find the slope of each line. a) b)

Closure Question Draw examples of lines with the following slopes: positive negative zero undefined

Section 6-5

Warm – Up: Find the slope of the line that passes through each pair of points. 1. (-2, 7), (6, 1) 2. (2, 8), (- 4, 8) 3. (3, -2), (-5, - 4)

4. (-3, -1), (-3, 5)

Objective: To graph and write linear equations using point-slope form

You can use the definition of slope to find a form of a linear equation called point-slope form.

2 1

2 1

y ym

x x−

=−

* point-slope form: y – y1 = m(x – x1)

Example #1 Write an equation in point-slope form for the line through the given point that has the given slope.

a) (7, 4); m = -2 b) (6, -5); m =23

Example #2 Graph each equation.

a) ( )12 13

y x− = − + b) ( )35 24

y x+ = +

Example #3 Write an equation in point-slope form for the line passing through the given points. a) (2, 3), (-1, -5) b) (1, -3), (- 4, 7) Example #4 Write an equation of each line in point-slope form. a) b)

Closure Question Write an equation of a line in point-slope form and then graph your equation.

Section 6-2

Warm – Up: Graph each equation.

1. 31 ( 4)2

y x− = + 2. 14 ( 3)2

y x+ = − −

Write an equation in point-slope form for the line passing through the given points.

3. (5, 1) and (-2, -3) 4. (2, - 6) and (-3, 4)

Objective: To graph and write linear equations in slope-intercept form

* slope-intercept form: y = mx + b Example #1 Write each equation in slope-intercept form.

a) 15 ( 4)2

y x+ = − + b) 21 ( 6)3

y x− = −

Example #2 What are the slope and y-intercept of 2 3y x= − ?

x

y

x

y

Example #3

Write an equation of the line with slope 25

− and y-intercept 4.

Example #4 Graph the following equations.

a) 4 1y x= − b) 3 22

y x= − +

Example #5 Write the equation for the line in slope-intercept form. Example #6 Given two points on a line, write the equation of the line in slope-intercept form. a) (-1, -9) and (2, 3) b) (4, -1) and (8, -3) Closure Question How does changing the value of m affect the graph of a line?

How does changing the value of b affect the graph of a line?

x

y

x

y

Section 6-4

Warm – Up: Evaluate each expression. 1. 3 6 12x y− = for 0x = 2. 3 6 12x y− = for 0y =

3. 2 6 18x y− + = for 0x = 4. 2 6 18x y− + = for 0y =

Objective: To write linear equations in standard form and to graph using x- and y-intercepts

* standard form: Ax + By = C (A, B, C will be integers) (use x- and y-intercepts to graph)

Example #1 Write each equation in standard form.

a) 1 5( 3)y x− = + b) 1

4 ( 6)2

y x+ = − −

Example #2 Find the x- and y-intercepts of each equation. a) 3 15x y− = b) 2 6 8x y− = − Example #3 Graph each equation using x- and y-intercepts. a) 2 3 12x y− − = − b) 10 5 25x y− =

x

y

x

y

Example #4 Graph each equation. Tell whether the line is horizontal or vertical. a) 3x = − b) 4y =

Example #5 Write each equation in slope-intercept form, then graph the line. a) 2 5 15x y− = b) 3 4 24x y− − = −

3 Ways to Graph Lines:

* point-slope form: 1 1

( )y y m x x− = − (use point and slope to graph)

* slope-intercept form: y mx b= + (use slope and y-intercept to graph)

* standard form: Ax + By = C (use x- and y-intercepts to graph)

Closure Question How do you find the x- and y-intercepts of a linear equation?

x

y

x

y

x

y

x

y

Section 6-8

Warm – Up: Simplify each expression.

1. 2 7− 2. 12 8− 3. 30 48− 4. 24 12− +

Make an input-output table to graph the equation.

5. y x= Objective: To translate the graph of an absolute value equation absolute value equation: an equation whose graph is V-shaped

y x= (parent graph) translation: a shift of a graph horizontally, vertically, or both (The result is a graph of the same shape and size, but in a different position.) Do the exploration together as a class with your graphing calculator.

Example #1

Graph each function by translating y x= .

a) 3y x= − b) 5y x= +

x

y

x

y

x

y

Example #2

Write an equation for each translation of y x= . a) left 8 units b) right 4 units Example #3

Graph each function by translating y x= .

a) 2y x= + b) 6y x= −

Example #4

Write an equation for each translation of y x= . a) down 7 units b) up 1.5 units Example #5

Graph each function by translating y x= .

a) 1 5y x= + − b) 4 2y x= − +

Closure Question

Explain the difference between the graph of 3y x= + and the graph of

3y x= + .

x

y

x

y

x

y

x

y