Name Score Algebra 1B Assignments Chapter 6: Linear Equations (All graphs must be drawn on GRAPH PAPER!) Review Review Worksheet: Rational Numbers and Distributive Propert Worksheet: Solving Equations Quiz Rational Numbers, Distributive Propert, 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 Test Worksheet: Chapter 6 Review 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 b plugging solution into original equation Eample #1 Solve the following equations. Check our answers. a) 2( 4) = 12 b) 2 5 13 3 + = Eample #2 Solve the following equations. Check our answers. a) 5m 3 = 2m + 12 b) 6 g (2g 9) = 8 Eample #3 Solve the following equations. Check our answers. a) c 3 e+ 4 e 2 = b) = 3 4 5 7
Eample #4 Solve the following equations. Check our answers. a) 2 a+ 1 a = 7 b) 4(2 3) = 5( + 6) 3 3 2 Eample #5 Solve the following equations. Check our answers. a) 13 6v 5 = v + 10 7v b) 7 8 = 2(4 3) + 1 * no solution: no value of the variable will make the equation true (all variables cancel, left with NOT TRUE ) * identit: all values of the variable will make the equation true (all variables cancel, left with TRUE ) Eample #6 You work for a deliver service. With Plan A ou earn $5.00 per hour plus $0.75 per deliver. With Plan B ou earn $7.00 per hour plus $0.25 per deliver. How man deliveries must ou make per hour with Plan A to make as much mone as Plan B? Closure Question What order of operations should ou use to solve multi-step equations?
Section 6-1 Warm Up: Write in simplest form. 1. 7 3 2. 3 5 3 1 6 0 3. 8 ( 4) 3 7 4. 1 2 0 5 5. 0 1 1 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 Eample #1 For the data below, is the rate of change for each pair of consecutive das the same? What does the rate of change represent?
Eample #2 Find the rate of change of the data in the graph. * vertical change rise slope = rate of change = = = horizontal change run Eample #3 Find the slope of each line. a) b) 2 1 2 1 Eample #4 Find the slope of the line through each pair of points. a) (3, 2) and (5, 10) b) (-1, 4) and (3, -2) Eample #5 Find the slope of each line. a) b) Closure Question Draw eamples 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 pointslope form. 2 1 2 1 = m * point-slope form: 1 = m( 1 ) Eample #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 = 2 3
Eample #2 Graph each equation. 1 3 a) 2 = ( + 1) b) + 5 = ( + 2) 3 4 Eample #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) Eample #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 our equation.
Warm Up: Graph each equation. 1. Section 6-2 3 1 = ( + 4) 2. 2 1 + 4 = ( 3) 2 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: = m + b Eample #1 Write each equation in slope-intercept form. a) 1 + 5 = ( + 4) b) 2 2 1 = ( 6) 3 Eample #2 What are the slope and -intercept of = 2 3?
Eample #3 2 Write an equation of the line with slope and -intercept 4. 5 Eample #4 Graph the following equations. a) = 4 1 b) 3 = + 2 2 Eample #5 Write the equation for the line in slope-intercept form. Eample #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?
Section 6-4 Warm Up: Evaluate each epression. 1. 3 6 = 12 for = 0 2. 3 6 = 12 for = 0 3. 2 + 6 = 18 for = 0 4. 2 + 6 = 18 for = 0 Objective: To write linear equations in standard form and to graph using - and -intercepts * standard form: A + B = C (A, B, C will be integers) (use - and -intercepts to graph) Eample #1 Write each equation in standard form. a) 1 = 5( + 3) b) 1 + 4 = ( 6) 2 Eample #2 Find the - and -intercepts of each equation. a) 3 = 15 b) 2 6 = 8 Eample #3 Graph each equation using - and -intercepts. a) 2 3 = 12 b) 10 5 = 25
Eample #4 Graph each equation. Tell whether the line is horizontal or vertical. a) = 3 b) = 4 Eample #5 Write each equation in slope-intercept form, then graph the line. a) 2 5 = 15 b) 3 4 = 24 3 Was to Graph Lines: * point-slope form: = m( ) 1 1 (use point and slope to graph) * slope-intercept form: = m + b (use slope and -intercept to graph) * standard form: A + B = C (use - and -intercepts to graph) Closure Question How do ou find the - and -intercepts of a linear equation?
Warm Up: Simplif each epression. Section 6-8 1. 2 7 2. 12 8 3. 30 48 4. 24 + 12 Make an input-output table to graph the equation. 5. = Objective: To translate the graph of an absolute value equation absolute value equation: an equation whose graph is V-shaped = (parent graph) translation: a shift of a graph horizontall, verticall, or both (The result is a graph of the same shape and size, but in a different position.) Do the eploration together as a class with our graphing calculator. Eample #1 Graph each function b translating a) 3 =. = b) = + 5
Eample #2 Write an equation for each translation of =. a) left 8 units b) right 4 units Eample #3 Graph each function b translating a) 2 =. = + b) = 6 Eample #4 Write an equation for each translation of =. a) down 7 units b) up 1.5 units Eample #5 Graph each function b translating =. a) = + 1 5 b) = 4 + 2 Closure Question Eplain the difference between the graph of 3 = + 3. = + and the graph of