1. WARTIME BATTLE Solving Equations by Graphing

2. You’re in the Navy NOW  Identify where to place mines to sink enemy ships  Know path of our vessel  Know path of enemy vessels  Determine graphically then mathematically optimal mine locations  Note: you are not the captain of the vessel and cannot change your course

3. Review Graphing Lines  3x + 2y = 12  Graph using intercepts X intercept, y=0 3x +2(0) = 12 3x = 12 x = 4 Y intercept, x=0 3(0) +2y = 12 2y = 12 y = 6

4. Review Graphing Lines  3x + 2y = 12  Graph using y=mx+b  3x + 2y = 12  -3x  2y = -3x + 12  Divide by 2  y= -3/2x + 6  Y intercept = 6  Slope = -3/2

5. Get Started  Graph Battleship Course  Ask for check  Graph Enemy Courses  Calculate point to place mines  Might need to Estimate

6. Paths Enemy Path 1 Enemy Path 3 Enemy Path 2Mine # 1,( -7.5, 2.5) Mine # 2,( 0.5, -5.5) Mine # 3,( 4,-9)

7. Verify Mathematically  x + y = -5  y = -x – 5  Estimated point (4, -9)  -9=-(4) – 5  -9 = -9  2x + y = -1  y = -2x – 1  Estimated point (4, -9)  -9 = -2(4) – 1  -9= -8 -1  -9 = -9 Battleship PathEnemy Path 3

8. Solve Mathematically  x + y = -5  y = -x – 5  2x + y = -1  y = -2x – 1 Battleship PathEnemy Path 3 -x – 5 = -2x – 1 +1 +x -4 = -x 4 = x Estimated point (4, -9) y = -x – 5 y = -(4) – 5 y = -9

9. Verify Mathematically  x + y = -5  y = -x – 5  Estimated point (-7.5, 2.5)  2.5=-(-7.5) – 5  2.5 = 7.5-5  2.5=2.5  x – 3y = -15  y = 1/3x +5  Estimated point (-7.5, 2.5)  2.5 = 1/3(-7.5) +5  2.5= -2.5+5  2.5=2.5 Battleship PathEnemy Path 1

10. Solve Mathematically  x + y = -5  y = -x – 5  x – 3y = -15  y = 1/3x +5 Battleship PathEnemy Path 1 -x – 5 = 1/3x +5 -5 +x -10 = 4/3x -10(3/4) = x -7.5 = x Estimated point (-7.5, 2.5) y = -x – 5 y = -(-7.5) – 5 y = 7.5-5 y=2.5

11. Solve Mathematically  x + y = -5  y = -x – 5  4x – y = 7  y = 4x – 7 Battleship PathEnemy Path 2 -x – 5 = 4x – 7 +7 +x 2 = 5x 2/5 = x 0.4 Estimated point (0.4, -5.4) y = -(0.4) – 5 y = -.4 – 5 y = -5.4

12. Verify Mathematically  x + y = -5  y = -x – 5  Estimated point (0.4, -5.4)  -5.4 =-(0.4, ) – 5  -5.4 = -5.4  4x – y = 7  y = 4x – 7  Estimated point (0.4, -5.4)  -5.4= 4(0.4) – 7  -5.4 = 1.6 -7  -5.4 = -5.4 Battleship PathEnemy Path 2