**Assessment Question**

Danielle is playing the newest app on her phone, Algebra City Defense. Earlier in the game, you and Danielle helped the Mathonauts defend the city against a giant, three-headed monster. After defeating the monster, the game advances to Level Two! You and Danielle must help the Mathonauts blast off to their Interstellar Headquarters.

Question #1

Before blast-off, the Mathonauts must set the trajectory of their ship. Create a linear equation with a positive slope to be your original trajectory.

Question #2

After blast-off, the sensors have picked up an incoming meteor. The Mathonauts frantically start preparing for impact. If the linear equation of the meteor’s path is known, describe to the captain how to solve where your equation from question 1 and the meteor’s path will cross. Explain any possible methods used in discovering a solution.

question # 3

Having survived the meteor impact, thanks to some last-minute evasive maneuvers, the Mathonauts now set their sights on their Interstellar Headquarters. The Interstellar Headquarters orbits the Earth based on the equation y2 + x2 = 40,000. Using the original trajectory of the ship and complete sentences, explain to the pilot how to find where the ship’s path will cross the Interstellar Headquarters’s path.

question 4

While docked, the captain wants to resupply the ship’s missiles and ray-guns. You will need to explain to the captain what information you must know and how that can be used to determine the number of missiles and ray-guns to fill the ship and use all the batteries.

question # 5

Before departing the Interstellar Headquarters, the ship’s navigator begins to plan the next trip. She uses a map with their current trajectory already graphed on it. There is also a table that has coordinate points of a satellite that the Mathonauts must intercept. Explain to the navigator how she can use the graph and table to find where they will intercept the satellite. Assume the path of the satellite is linear. Use the coordinates to create an equation representing the path of the satellite. Explain the process and show how to find the point of intersection algebraically.

question #6

The navigator has to program the ship’s computer so that it will be prepared to intercept the satellite. To program it, the satelite’s path is set equal to the ship’s. The programmed equation is –4x – 2 = –x + 3. Explain to the navigator how the programmed equation can be graphed to find the point of intersection. Use complete sentences.

Now the Mathonauts are ready to blast off and save the day once again, thanks to your help!

Fin!

**presentation**

**By :Holguy Rinchet**

I've created this equation :

y=2x+4

If we know the equation for the meteor and the astronauts we could easily solve by graphing or subtitutio.

At this point the pilot want to find where these two direction cross or where they meet in order to do that we must use the 2 equations y2 + x2 = 40,000 and y=2x+4 , we would have to graph them to find the intersection Or where the meet.

To resupply the captain must find how many batteries it takes for the ray guns and the missile to function, I would set an equation ( let R represent ray guns , M represent missiles, while x is the amount of battery required and Y is the battery for ray guns .

The equation would be

( R+m=15) and & xr +my=45

they have to find the equation and their are lots of way to find it the easiest and most simplest i know is by first finding the slope y2-y1 / x2 -x1 the 2 points I'm using is (3,2) and (2,1 ) when substitute with the variable it will equal to 1.

In order to turn it into an equation It has to be in the form of y=mx+b

y=1 m = 2 B= -1

1=1(2)+b which is -1

the final equation is y =x-1

The equation is -4x-2 = - x +3

add x to both side of the equation

which results to -3x then bring down the 2 and the 3

the equation will be -3x-2=3 at this point it becomes a simple equation to solve just by addi 2 to both sides which eliminate the -2 on the right.

-3x=5 use the division property , the -3x is canceled which leaves -5/3 then i can plug in to find the y .