ࡱ> |~{nn_ .bjbj 7bb&& ajjTTTtp!4Tv"d&&&&$$$$h$x$$$&&0$V&&$q&:`,F0vrBX$$$$$$$B$$$v$$$$$$$$$$$$$j : CC Math I Standards: Unit 5 SLOPE-INTERCEPT FORM: Part 1 Warm Up Activity: Find slope of (3, 12) and (6, -6) Find slope of (4, 8) and (-5, 8) Find slope of (-5, 2) and (7, 6) What is the Y INTERCEPT of a line? The POINT where the line crosses the y axis is called the y-intercept = (0, b)  Identify the y-intercept of each line Y-AXIS: vertical axis Follow the line until it reaches y- axis Draw Intercept point Find the coordinate of that point Example: Line #1: Line #1 cross the y-axis at (0 , 5) Line #2: Line #3: Line #4: Line #5: Line #6: Line #7: What is Slope-Intercept Form? Identify the Slope and Y-Intercept in each of the following equations: y = 3x + 5 y = 7 + 9x -4x 3 = y  EMBED Equation.3  y = 112 + 87x 0.4x 2 = y  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  6 7x = y y = 23 Write the Equation of a line given slope and y intercept: 1) b = 17/5 and m = 3 3) m = and (0, -6) 5) b = 5/7 and m = -3/7 2) Slope of 3 and y intercept is 5. 4) Slope of -2 and (0, 4) 6) Y intercept is -2 and slope is - . Write the Equation of a line in each graph: IDENTIFY the y-intercept (b) of the line and the slope (m) of the line WRITE y = mx + b equation by substituting m and b values.  SHAPE \* MERGEFORMAT  1) Slope: Y Intercept: Equation:  SHAPE \* MERGEFORMAT  2) Slope: Y Intercept: Equation:  SHAPE \* MERGEFORMAT  3) Slope: Y Intercept: Equation:  SHAPE \* MERGEFORMAT  4) Slope: Y Intercept: Equation:  SHAPE \* MERGEFORMAT  5) Slope: Y Intercept: Equation:  SHAPE \* MERGEFORMAT  6) Slope: Y Intercept: Equation: GRAPHING LINES BY HAND: How do you graph a line in slope intercept form? PLOT the y intercept. From y intercept perform SLOPE (RISE over RUN) to plot a second point. Draw a line between the two points. 1)  EMBED Equation.3  y-intercept = Slope = Rise = Run =  2)  EMBED Equation.3  y-intercept = Slope = Rise = Run = 3) y = 1 4x y-intercept = Slope = Rise = Run = 4) y = 3x - 2 5)  EMBED Equation.3  y-intercept = Slope = Rise = Run =  6)  EMBED Equation.3  y-intercept = Slope = Rise = Run = 7)  EMBED Equation.3  y-intercept = Slope = Rise = Run = 8)  EMBED Equation.3  CC Math I Standards: Unit 5 SLOPE-INTERCEPT FORM: Part 2 1) Identify the SLOPE and Y-INTERCEPT in each equation: 1a.  EMBED Equation.3  1b.  EMBED Equation.3   1c.  EMBED Equation.3  1d.  EMBED Equation.3  1e.  EMBED Equation.3  1f.  EMBED Equation.3   2)Write the SLOPE-INTERCEPT FORM for each line: Line #1 Equation: Line #2 Equation: Line #3 Equation: HOW DO YOU DETERMINE IF A POINT IS ON A LINE? For each point (x, y), SUBSTITUTE the x-value and y-value into the equation. CHECK if both sides of the equation If EQUAL SIDES, then point IS on line If NOT EQUAL SIDES, the point IS NOT on line Example: y = 3x 4 Check: (1, -1) (2, 6) (-3, 13) (-4, -16) (5, 11) PRACTICE PROBLEMS: 1)  EMBED Equation.3  Check: (1, 12) , (-3, 21), (2, 11) 2)  EMBED Equation.3  Check: (-2, -7), (3, 44), 6, 25) 3)  EMBED Equation.3  Check: (8, 1), (4, 3), (-6, 2) 4)  EMBED Equation.3  Check: (12, -16), (-4, 4), (4, 4) 5)  EMBED Equation.3  Check: (3, -1) , (1, -5) , (0, 8) 6)  EMBED Equation.3  Check: (6, 3), (-3, -1), (-9, -5) REVIEW: Graph a line for each of the following for a given point and a slope. 1) point = (0, -2); m = 5/2  2) point = (2, 1) ; m = -3/2  3) point = (-3,4); m = -1 Based on graphs above, write equation of each line in SLOPE-INTERCEPT FORM: 1) 2) 3) How do we find the equation of a line without graphing? CASE #1: FIND THE Y-INTERCEPT of a line when you have the slope and any point. What is the equation for slope-intercept form? Example #1: Line that passes through (1, 5) and has a slope of 2. Step #1: SUBSTITUTE known values into slope- intercept form Step #2: SOLVE for b. Step #3: WRITE the equation with x and y as variables Example #2: Line that passes through (2, -3) with slope of . Step #1 and 2: Step #3: Equation Find Equation in Slope-Intercept Form Example 3: Line that passes through (1, -4) with a slope of 5/2. Step #1 and 2: Step #3: Equation Example 4: Line that passes through (5, 5) with a slope of 1/3. Example 5: Line that passes through (-9, 8) with a slope of -5/3. Example 6: Line that passes through (-3, -7) and m = 4. SPECIAL CASE: UNDEFINED SLOPE 1) Write an equation of a line that passes through (1, 3) with a slope of UNDEFINED. 2) Write an equation of a line with an undefined slope through the point (-2, 12). 3) Write an equation of a line has y-intercept of 5 with an undefined slope. CLASSROOM WORK: Use a separate piece of paper, Write an equation of a line that passes through each point with the given slope. (-3, 3) and m = 1; (0, 6) and slope = -2; (1, 6) and m = ; m = -3/5 and (4, -3); (5, -3) and slope = 3/2; (4, -2) and m = 0; CC Math I Standards: Unit 5 Review of Last Week 1) State the SLOPE Formula: 2) Find the slope of the line for each pair of points: 2a. (3, 4) and (5, 8) 2b. (-2, -9) and (-3, -6) 2c. (6, -4) and (8, -4) 2d. (2, 3) and (-5, -1) 2e. (7, 2) and (7, -2) 2f. (-5, 7) and (1, -2) 3) State the SLOPE INTERCEPT FORM Equation for a line: 4) For each graph, FIND the slope and y-intercept to write the equation of the line:  SHAPE \* MERGEFORMAT  5) For the given point (x, y) and slope, m, find the SLOPE INTERCEPT FORM of line. STEP by STEP Example: (4, 2) and slope = 3 What do you know?Substitute and SolveWrite Equationy = 2 x = 4 m = 3 b = ?? y = mx + b 2 = 3*4 + b 2 = 12 + b -10 = by = mx + b y = 3x 10 Keep x and y as variables.  5a. (0, 1) and slope = 1/3 5b. m = -2 and (-1, 3) 5c. (-5, -3) and  EMBED Equation.3  5d. (10, -3) and m = 0 5e. (9, 11) and  EMBED Equation.3  5f. slope = 4 and (0, -7) 5g. (14, 6) and  EMBED Equation.3  5h. (2, -4) and m = -1 5i.  EMBED Equation.3 and (6, 7) CC Math I Standards: Unit 5 SLOPE-INTERCEPT FORM: Part 3 Find the SLOPE-INTERCEPT FORM of a line when given ANY two points on the line? 3 STEP PROCESS: Given two points (x1, y1) and (x2, y2) on a line Step 1: FIND the SLOPE of line:  EMBED Equation.3  (REDUCE FRACTIONS!!!!) Step 2: PICK one point and the slope to FIND the Y-INTERCEPT. (x1,y1) and m Find the y-intercept (b) for y1 = m x1 + b (REDUCE FRACTIONS!!!!) Step 3: WRITE the equation of the line in SLOPE-INTERCEPT FORM. Use the m from Step 1 and b from Step 2 y = mx + b STEP BY STEP: Find the Slope Intercept Form of the line through (5, 7) and (3, 1). #1: SLOPE#2: Y-INTERCEPT#3: EQUATION(5, 7) and (3, 1).  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  and (5, 7) y = mx + b  EMBED Equation.3  -8 = by = mx + b y = 3x 8 Keep x and y as variables. Example 1: Find the Slope Intercept Form of the line through (-3, 2) and (5, -14) Example 2: Find the equation of the line that passes through (4, 7) and (8, 12). Example 3: Find the equation of the line that passes through (0, 6) and (5, 0). Example 4: Find the Slope Intercept Form of the line through (3, 4) and (-2, 4). Example 5: Find the Slope Intercept Form of the line through (-1, 3) and (4, -1). SPECIAL CASE: Find the equation of the line that passes through (-1, 3) and (-1, -8). CLASSWORK PRACTICE: Use Separate paper as needed. Find the Slope Intercept Form of the line through each of points. 1. (3, -5) and (6, 4) 2. (-2, 20) and (2, 4) 3. (0, -3) and (2, 0)4. (2, -4) and (2, 6) 5. (-4, -5) and (6, -1) 6. (3, -3) and (1, -3) 7. (6, 2) and (4, 4) 8. (4, 5) and (-3, -1) 9. (-2, -7) and (8, 8) CC Math I Standards: Unit 5 SLOPE-INTERCEPT FORM: Part 4 Find Slope Intercept Form of a Line when given a Linear Equation Y Coefficient of One Case SIMPLIFY and MOVE x terms or number terms by addition or subtraction For Problems #1 6: SOLVE for y, then IDENTIFY the Slope and Y-Intercept 3x = 5 + y y 8 = 2x + 3  EMBED Equation.3  7 = 6x + y 2 5(7 x) = y y 3x + 5 = 12 For Problems #7 12: Find Slope Intercept Form AND GRAPH the Line Identify the Slope and Y-Intercept 1 = -3x + y  SHAPE \* MERGEFORMAT  y + 7 = x + 3  SHAPE \* MERGEFORMAT  2(x 2) = y  SHAPE \* MERGEFORMAT   EMBED Equation.3   SHAPE \* MERGEFORMAT  -2x + y = 0  SHAPE \* MERGEFORMAT   EMBED Equation.3   SHAPE \* MERGEFORMAT  CC Math I Standards: Unit 5 SLOPE-INTERCEPT FORM: Part 5 Find Slope Intercept Form of a Line when given a Linear Equation Non-One Coefficients of y Case Simplify both sides (if needed) Move x terms or constants by addition or subtraction to one side Divide all terms by the coefficient of y REDUCE All Fractions Example 1: 3y + 6x = 10 Example 2: 10y 5x = 8 Example 3: 8x 4y = 12 Practice Problems: Solve for Slope Intercept Form and Identify the slope and y-intercept 9y 3x = 18 8x - 2y = 7 14y 35x = 63 x 5y = 6 x + 5y = 8 21 = 7y 2x 15 = -7x + 6y 9 = 4y x 9x + 3y = 0     y Line #1 Line #2 Line #3 Line #5 Line #7 Line #6 Line #4 x LINE #1 LINE #2 LINE #3 089JKPZmn' - . / 0 wrhULhL 5>*CJ$jhS5>*UmHnHtH uhSh<5CJ h<5jh4UmHnHuh9h5>*CJh9h#85>*CJ hJ5>* hO5>*hOhJ5ho# h#85 h)55 h:5hL h:5>*CJ\h5>*CJ\hT^5>*CJ h8 h\5>*CJ h#856 hW569Kn. 0 V l  & Fgd  & Fgd8  & FgdhOgd $a$gd2 `gdOh^hgd: & Fh^hgdegdW$a$gd\$a$0 U V ] k l               䮦|pdZSZpIShf0hbB_5CJ ho#5CJhf0h8 5CJhf0h8 5>*CJhf0h 5>*CJ.jhf0h45>*CJUmHnHtH u h8 5>* hhOh hQ,gh8 h8 5h8 hQ,g5hhOh 5>* hhhOh8 hhOhhOh8 hhO>*hhOhhO5>*hhO hhO5>* h 5>*h h 5>*    8 9 R S T u v x y { | d^gdG- & FdgdG- & Fgdp $a$gd2 gddgdbB_gd   ) * + , 4 5 6 8 9 B F O P Q R S T q s t u v w x y z { | 鸬ytmthc hUj5 h5-5 hvK hp hp 5h8 hp 5>*CJ h#85>* hvK h#8h8 ho#h ho#CJ h8 5CJh8 h5>*CJhhOh8 5>*hf0h8 5>*CJhf0hbB_5CJ ho#5CJhf0h8 5CJhf0h 5>*CJhf0h 5CJ%     * , - . 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L^`LhH.h^`OJQJo(hHhp^p`OJQJ^Jo(hHoh@ ^@ `OJQJo(hHh^`OJQJo(hHh^`OJQJ^Jo(hHoh^`OJQJo(hHh^`OJQJo(hHhP^P`OJQJ^Jo(hHoh ^ `OJQJo(hHH H^H` o() ^`hH. pLp^p`LhH. @ @ ^@ `hH. ^`hH. L^`LhH. ^`hH.SummaryInformation(DocumentSummaryInformation84MsoDataStoreP(::GRQA5SJWW3YQ==2P(:: D P \ ht| Algebra I Chapter 5 Section 3 wfut602006NormalSmith, Matthew J21Microsoft Office Word@2~@Nb@UF@f% u ՜.+,0 hp|  WFUE& Algebra I Chapter 5 Section 3 Title   F Microsoft Word 97-2003 Document MSWordDocWord.Document.89q ^`hH. PLP^P`LhH.z^`zo()^`.pLp^p`L.@ @ ^@ `.^`.L^`L.^`.^`.PLP^P`L.h^`OJQJo(hHh^`OJQJ^Jo(hHohp^p`OJQJo(hHh@ ^@ `OJQJo(hHh^`OJQJ^Jo(hHoh^`OJQJo(hHh^`OJQJo(hHh^`OJQJ^Jo(hHohP^P`OJQJo(hHH H^H` o() ^`hH. pLp^p`LhH. @ @ ^@ `hH. ^`hH. L^`LhH. ^`hH. ^`hH. 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