Quarter+1+Project

Task 1: 4) Yes, the graph does increase. If you look on the x-axis at about 8 seconds and then look up at the white line, you see that it increases.

5) Yes, the domain of the horizontal line on the graph is [15, 31]. From 15 seconds to 31 seconds, the spaceship continues to go 25.5 meters per second which means the spaceship moved at the same speed for 16 seconds. This could be because there were no obstructions in the spaceship's path for those 16 seconds or because the astronaut piloting the spaceship left it on cruise control so it traveled at the same speed for 16 seconds.

6) I know that the spaceship reached planet x because planet x is located at about 36 seconds on the x-axis and the spaceship eventually makes it to that point on the graph.

7) The spaceship had to travel 85.36 meters to get to planet x. To find this, I subtracted 5.04, the distance the spaceship traveled when it reached planet x, from 90.4, the spaceship's distance 0 seconds in.

8) At 0 seconds into the spaceship's journey, it is traveling at a speed of 90.4 meterss per second. Its distance per meter decreases until 8 seconds in when it begins to travel more meters than the 7 second mark. At 15 seconds, the spaceship continuously travels at 25.5 meters per second until 32 seconds. At the 35 second mark, the distance it travels per second greatly increases as the spaceship nears planet x.

10) Up until the 9 second mark, player 2 has a negative slope. Then the spaceship has a positive slope up until the 14 second mark. Then it has a negative slope for the rest of the spaceship's journey.

11) No there is no vertical line on the graph. If there were a vertical graph on the line, this would mean that over a period of time the spaceship stopped moving and if that were to happen then the spaceship would fall out of the sky. So, it is not possible for there to be a vertical line on the graph.

12) No, it is not possible to make the line zig-zag back and forth because for that to happen the spaceship would have to travel back in time which is not possible.

Task 2:

1) (0,9), (1,10), and (-1, 9) are all solutions to the system of inequalities.

2) (-2,6) is a point that is a solution to one of the inequalities but not the other one.

4) The purple shading switches to the other side because moving the line changes where the solutions to the inequality are. So if the solutions are in a different spot than before, a different spot will be shaded.

5) You would have to change the inequality to Y ≥ -13.2x + 7.27 to keep the purple shading on the right of the line.

10) 11) The blue green points (0,-2) and (3,-3) are solutions to the system of inequalities because they fall in the section of the graph where the two colors intersect.

12) Students may think that the points (0,1) and (1,3) are solutions but that is incorrect. Points on a line are solutions so they might think that those points are solutions to the system but to be a solution to a system, the points have to be in the section that is colored by both colors, not just one.

16) If this were a system of equations, the solution would be (-3, 5) because that is the point where the lines intersect.

17) y = -0.5x+3.5

Plug in one y of the point.

5= -0.5x+3.5 -3.5 -3.5

1.5=-0.5x /-0.5 /-0.5

x=3

Task 3: The first coordinates I chose were (2,6).