Monday October 3 rd Wrap up of Chapter 3 -some people need to take Ch 3 test -some need to finish Ch 3 test -others can work on extra credit 3.8 chapter review Chapter 4 Graphing Linear Equations 4.1 Coordinates and Scatter Plots Example 1: Plot and label the points: A(2,1), B(5,03), C(-3,0), D(-2,-2), E(0,4), F(-2,3) Label axes Label scale Example 2: The data below represent the weight and height of a male. At age 13, he was 63 in. tall. Predict his weight at age 13. AgeHeight (in.) Weight (lb) MondayTuesdayWednesdayThursdayFriday 3 A Ch 3 wrap-up 4 A H D A A H E PSAT-no class 13 A A Quiz New 4.6; End of 1/4 17 A C H A Review 21 D Ch 4 Test Date Assigned-due next dayAssignment 10/4 Tuesday4.1 p #10-26 even, 27-32, /5 Wednesday4.2 p #12-50 even 10/6 Thursday4.2 p215 #52,54,60,62,64,66,67-70 and /7 Friday4.3 p221 #14-40 even, 41-43 How can we graph an equation? 4.2 Graph an equation by using a table of values 4.3 Graphing Using Intercepts 4.6 Graphing Using Slope Intercept Form: y=mx+b Find the x and y intercepts of 4x+3y=12 Solution: 4x + 3(0) = 12 (substitute 0 for y) 4x = 12 x = 3 The x intercept is 3. The line crosses the x axis at (3,0). 4(0) + 3y = 12 (substitute 0 for x) 3y = 12 y = 4 The y intercept is 4. The line crosses the y axis at (0,4). Use the intercepts to graph the line. By sure to label your axes and mark your scale. Graph x 2 =4y Solution: x 2 = 4(0) (substitute 0 for y) x 2 = 0 The x intercept is 2. The line crosses the x axis at (2,0). 0 2 = 4y (substitute 0 for x) -2 = 4y y = - 1/2 The y intercept is -1/2. The line crosses the y axis at (0,-1/2). Use the intercepts to graph the line. By sure to label your axes and mark your scale. Graph y = -2x + 25 Solution: 0 = -2x +25 (substitute 0 for y) 2x = 25 x = 12 1/2 The x intercept is 12 1/2 The line crosses the x axis at (12.5,0) y = -2(0) + 25 (substitute 0 for x) y = 25 The y intercept is 25. The line crosses the y axis at (0,25). What is you scale for graphing the line? Monday October 10 th Bellwork: p224 #1, 5, 11 1.Plot and label the ordered pairs in a coordinate plane: A(-4,1), B(0,2), C(-3,0) Find three different ordered pairs that are solutions of the equation. Graph the equation. P 224 #5) y=2x-6 XY 02(0)-6=-6 32(3)-6=0 12(1)-6=-4 Find the x and y intercept of the line. Graph the line. Lable the intercepts. 11) y=4-x y=4-0 (insert 0 for x to find y intercept) y=4 y intercept= (0,4) 0=4-x (insert 0 for y to find x intercept) x=4 x intercept = (4,0) MondayTuesdayWednesdayThursdayFriday 3 A Ch 3 wrap-up 4 A H D A A H E PSAT-no class 13 A A Quiz New 4.6; End of 1/4 17 A C H Review 20 A Review 21 D Ch 4 Test Date Assigned-due next dayAssignment 10/7 Friday4.3 p221 #14-40 even, /10 Monday4.3 day 2 p221 #44-58 even, all 10/11 Tuesday4.4 p230 16,18,20,24,28,32,36,37,38,42,46,49,52-55, /12 WednesdayNo class because of PSAT 10/13 Thursday4.5 p237 #12-20 even, 21,24,26,28,30,33 10/14 Friday4.6 p244 #14-50 even 4.4 The Slope of a Line 1. Find the slope of the line passing through (-3,0) and (-1,6) Given (x 1,y 1 ) and (x 2,y 2 ), find slope using m = y 2 -y 1 x 2 -x 1 2. Find the slope of the line passing through (-1,-3) and (5,-3) Given (x 1,y 1 ) and (x 2,y 2 ), find slope using m = y 2 -y 1 x 2 -x 1 3. Find the slope of the line passing through (-2,1) and (1,-3) Given (x 1,y 1 ) and (x 2,y 2 ), find slope using m = y 2 -y 1 x 2 -x 1 4. Find the slope of the line passing through (0,-1) and (0,4) Given (x 1,y 1 ) and (x 2,y 2 ), find slope using m = y 2 -y 1 x 2 -x 1 Given (x 1,y 1 ) and (x 2,y 2 ), find slope using m = y 2 -y 1 x 2 -x 1 Key concepts from 4.4 MondayTuesdayWednesdayThursdayFriday 3 A Ch 3 wrap-up 4 A H D A A H E PSAT-no class 13 A A Quiz New 4.6; End of 1/4 17 A C H A Review 21 D Ch 4 Test Date Assigned-due next dayAssignment 10/7 Friday4.3 p221 #14-40 even, /10 Monday4.3 day 2 p221 #44-58 even, all 10/11 Tuesday4.4 p230 16,18,20,24,28,32,36,37,38,42,46,49,52-55, /12 WednesdayNo class because of PSAT 10/13 Thursday4.5 p237 #12-20 even, 21,24,26,28,30,33 10/14 Friday4.6 p244 #14-50 even Why is slope important? Goals for today: 4.5 Direct variation Review for Friday quiz Two variables vary directly if k not = 0 and y=kx Think direct variation (y=kx) indirection variation (y=k/x) k=constant of variation, also the slope Ex.1) Find the constant of variation and the slope for the direct variation model y=-3x y=kx k=constant so k=-3 Ex. 2) The variables x and y vary directly. When x=-3, y=- 30 a)Write an equation that relates x and y y=kx -30=k(-3) k=10 y=10x b) Find the value of y when x=8 y=10x y=10(8) y=80 Ex 3) The income at a store varies directly as the advertising budget. When the owner spent $3000 per month on advertising, the monthly gross income was $120,000. If the owner increases the advertising budget to $5000, how much gross income should they expect? y=kx let x=$advertising and y=$gross 120,000=k(3000) k=40 y=40x If x=$5000, then: y=40(5000) y=$200,000 Or if 3000 = 5000,then 3000y=60,000,000 y=$200, y Monday, October 17 th Start of 2 nd quarter Chapter 4 Graphing Linear Equations 4.1 Coordinates and Scatter Plots How can we graph an equation? 4.2 Graph an equation by using a table of values 4.3 Graphing Using Intercepts 4.6 Graphing Using Slope Intercept Form: y=mx+b Given (x 1,y 1 ) and (x 2,y 2 ), find slope using m = y 2 -y 1 x 2 -x 1 Key concepts from 4.4 4.5 Direct variation Two variables vary directly if k not = 0 and y=kx Think direct variation (y=kx) indirection variation (y=k/x) k=constant of variation, also the slope MondayTuesdayWednesdayThursdayFriday 3 A Ch 3 wrap-up 4 A H D A A H E PSAT-no class 13 A A Quiz New 4.6; End of 1/4 17 A 4.6/ C H Review Girls retreat 20 A Review Boys retreat 21 D Ch 4 Test 10/14 Friday4.6 p244 #14-50 even 10/17 Monday4.6 p244 #52-58,62,63,71-76; 4.7p253 #11-14,16,18,20,32 10/18 Tuesday4.8 p all, even, all, even 4.8 p even 10/19 WednesdayReview for test; freshmen girls retreat 10/20 ThursdayReview for test; freshmen boys retreat 4.6 Graphing Using Slope Intercept Form Ex 1) Write the equation 3x + 4y =8 in slope-intercept form. Identify the slope and y-intercept. 3x + 4y = 8 -3x+4y = 8-3x 4y= -3x +8 y=(-3/4)x +2 Slope = -3/4 Y-intercept = 2 Ex 2) Graph -2x + y = 5 +2x+ y = 5 + 2x y= 2x + 5 slope = 2 y-intercept =5 Ex 3) Which of the following lines are parallel? a)3y= -9x -5 b)2y-6x= -5 c)12x +4y =1 a)y= -3x (5/3) b)2y=6x -5 y=3x (5/2) c)12x + 4y = 1 4y= -12x + 1 y= -3x + a) And c) are parallel because their slopes are the same. 4.7 Solving Linear Equations Using Graphs 5x+ 3 = -2 5x = x = -5 x= -1 5x = x + 5 = 0 y= 5x + 5 Slope = 5 y-intercept = 5 When plug in 0 for y, then x = -1. MondayTuesdayWednesdayThursdayFriday 3 A Ch 3 wrap-up 4 A H D A A H E PSAT-no class 13 A A Quiz New 4.6; End of 1/4 17 A 4.6/ C H Review Girls retreat 20 A Review Boys retreat 21 D Ch 4 Test 10/14 Friday4.6 p244 #14-50 even 10/17 Monday4.6 p244 #52-58,62,63,71-76; 4.7p253 #11-14,16,18,20,32 10/18 Tuesday4.8 p all, even, all, even 10/19 WednesdayReview for test; freshmen girls retreat 10/20 ThursdayReview for test; freshmen boys retreat 4.8 Functions and Relations Relation: any set of ordered pairs Function: for every input, there is exactly one output Function notation: f(x) Instead of: y=2x+4 f(x) = 2x+4 When we plug in 1 for x what do we get? f(1) = 2(1) +4 f(1) = 6 Input Domain x Output Range Y f(x) Evaluating a function for specific inputs: x=f(x)=10x+1f(x) 2f(2)=10(2)+1f(2)=21 0f(0)=10(0)+1f(0)=1 -3f(-3)=10(-3)+1f(-3)=-29 x=h(x)=h(x) 2h(2)= 0h(0)= -3h(-3)= 32. f(x)= -2x+5 Think of it like: y= -2x+5 Slope = -2 y-intercept = 5 42.) f(2) = -3, f(-2) = 5 Remember: m= y 2 -y 1 x 2 -x 1 (2, -3), (-2, 5) m= 5-(-3) = 8 = MondayTuesdayWednesdayThursdayFriday 3 A Ch 3 wrap-up 4 A H D A A H E PSAT-no class 13 A A Quiz New 4.6; End of 1/4 17 A 4.6/ C H Review Girls retreat 20 A Review Boys retreat 21 D Ch 4 Test 10/14 Friday4.6 p244 #14-50 even 10/17 Monday4.6 p244 #52-58,62,63,71-76; 4.7p253 #11-14,16,18,20,32 10/18 Tuesday4.8 p all, even, all, even 10/19 WednesdayReview for test; freshmen girls retreat 10/20 ThursdayReview for test; freshmen boys retreat