Slide 1

Straight Ahead! Slide 2 Straight Ahead WARM-UP! Graph the following lines on grid paper. y = 3x + 2 y = 8 (Hint: this line has NO slope) What point do these two lines have in common? Slide 3 y = 3x + 2 y = 8 (2, 8) Warm-up Solution! Slide 4 Straight Ahead Practice! Graph the following lines on grid paper. y = 4x + 1 y = 7 2x What is the SOLUTION? Remember, the solution is the point they have in COMMON! Slide 5 y = 4x + 1 y = 7 2x (1, 5) Practice Solution! Slide 6 Straight Ahead Quiz! Solve the following systems 1.y = 3x + 1a. ( -5, -2 ) b. ( -2, -5 ) y = -2c. ( 1.5, -2)d. ( 2, 7 ) 2.y = 2x 1a. ( 7, 4)b. ( 4, 7 ) y = 4c. ( -2, 4 )d. ( 4, -2 ) 3.y = 3 2xa. ( 0, 3 )b. ( 3, 0 ) y = x + 3c. ( 2.5, 5.5)d. ( 3, -2) 4.y = -x + 6a. (2, 4)b. (4, 2) y = 2xc. (6, 0 )d. (0, 0 ) 5.y = 4 xa. (2, 2)b. ( 0, 4) y = xc. (4, 0 )d. ( -2, -2 ) Slide 7 Straight Ahead Tutorial #1! Graph the following lines on grid paper. y = 7 8x y = -1 (Hint: this line has NO slope) What point do these two lines have in common? Slide 8 y = 7 8x y = -1 Howd you do? (1, -1) Slide 9 Straight Ahead Tutorial #2! Graph the following lines on grid paper. y = x - 7 y = -2x + 2 What point do these two lines have in common? Slide 10 y = x 7 y = -2x + 2 Howd you do? (3, -4) Slide 11 Uphill Slide 12 Tired of Graphing?? Remember your warm-up? Is there another way? Graph the following lines on grid paper. y = 3x + 2 y = 8 (Hint: this line has NO slope) What point do these two lines have in common? (2, 8) Slide 13 Uphill Practice Solve the same system without graphing! y = 3x + 2 y = 8 What if we SUBSTITUTE y with 8 and solve? = 3x + 2 - 2 - 2 6 = 3x 3 3 2 = x 8 y SAME PROBLEM! (2, 8) When y = 8, x = 2 (2, 8) Slide 14 NEW PROBLEM! same idea Solve the system without graphing. y = 4x + 1 y = 7 2x Like before, we can replace y with 7 2x. = 4x + 1 +2x +2x 7 = 6x + 1 -1 -1 6 = 6x 1 = x y 7 2x Uphill Practice Slide 15 WAIT! A solution to a system must have an x AND a y!!! We NOW know x = 1, so how can we solve for y ?? y = 7 2y = 4 + 1 y = 7 2y = 4 + 1 y = 5y = 5 The solution is ( 1, 5 )! x (1) (1, 5) x (1) Slide 16 Uphill Quiz! Show the first step of SUBSTITUTION to solving the following systems without graphing. 1.y = 3x + 1a. -2 = 3x + 1 b. y = 3 (-2) +1 y = -2c. y = -2x + 1d. 3 = -2x +1 2.y = 2x 1a. 4 = 2x 1 b. y = 3 (4) 1 y = 4c. y = 4x 1 d. 2 = 4x 1 3.y = 3 2xa. x + 3 = 3 2x b. x 2 = 3 + 3x y = x + 3c. y = 3x 2x + 3 d. 3 2x + x + 3 Solve the following systems without graphing. 4.y = 4xa. ( 1, 4 )b. ( 4, 1 ) y = -3x + 7c. ( 7, 4 )d. ( 4, 7) 5.y = 3x + 1a. ( -1, -2 )b. ( -2, -1 ) y = -2x 4 c. ( 4, -6 )d. ( -6, 4 ) Slide 17 Uphill Tutorial y = x + 14 y = -2x 7 = x + 14 y -2x - 7 - x -x -3x 7 = 14 + 7 + 7 -3x = 21 -3 x = -7 Slide 18 WAIT! A solution to a system must have an x AND a y!!! We NOW know x = -7, so how can we solve for y ?? y = -2 7y = + 14 y = 14 7y = -7 + 14 y = 7y = 7 The solution is ( -7, 7 )! x (-7) x Slide 19 So basically y = -2x - 7 y = x + 14 If you have two equations that both equal ___, you can _________ one y with the other expression and solve for ___ !!!! Slide 20 Mountainous Slide 21 The Dirty Dawg Salon Slide 22 Some day, you hope to be a veterinarian. Until then, you decide that washing dogs is the way to go. You purchase $24 in supplies (buckets, towels, hoses), and the cost of a special flea prevention shampoo comes out to $1 per dog washed. If x represents the number of dogs washed, determine the equation for the money spent washing dogs. y = 1x + 24 $1 PER dog $24 ONE TIME cost for supplies Slide 23 The Dirty Dawg Salon You charge $4 to wash each dog. Determine the equation for the money earned washing dogs. y = 4x $4 PER dog Slide 24 Mountainous Challenge! The system that represents this problem is y = x + 24 y = 4x Use what you have learned in this lesson to determine the minimum number of dogs you will need to wash to in order to make a profit. a.) 6b.) 8 c.) 9d.) 12 Slide 25 Mountainous Solution!! y = x + 24 y = 4x = x + 24 y 4x -x 3x = 24 3 x =8 Careful!!! This is the number of dogs youd have to wash to BREAK EVEN!! You would need 9 to actually make a profit! Solution: 9 dogs Slide 26 Mountainous Check After 8 Dogs! Money SpentMoney Earned y = + 24y = 4 y = $32y = $32 After 9 Dogs! Money SpentMoney Earned y = + 24y = 4 y = $33y = $36 You made $3! x (8) x x (9) x Slide 27 Celebration!!!