Question

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.

Answer 1

http://learn.flvs.net/webdav/educator_algebraII_v13/module06/images/06_04_assessment/06_04_01.jpg

x y
1 0
2 1
3 2

Answer 2

@hartnn

Answer 3

@phi

Answer 4

@ganeshie8

Answer 5

@Whitemonsterbunny17

Answer 6

@MaimiGirl

Answer 7

i can help
do u still need help

Answer 8

From the table, the three points are: (1,0), (2,1) and (3,2)
We can find the slope of this line: (y2-y1)/(x2-x1) = (1-0)/(2-1) = 1
y = mx + b
We found the slope m = 1
y = x + b
when x = 1, y = 0
0 = 1 + b
b = -1
The equation of the line representing the path of the satellite is: y = x - 1

Answer 9

We can also find the equation of the trajectory of the ship:
x / x_intercept + y / y_intercept = 1 is a equation of a line whose x and y intercepts are known. From the graph we can see the x and y intercepts are 2.5 and -5.
x / 2.5 - y / 5 = 1
multiply by 5
2x - y = 5
y = 2x - 5 is the equation of the line in the graph.

Find the intersection of the lines: y = x - 1 and y = 2x - 5
Equate the y's: x - 1 = 2x - 5
-1 + 5 = 2x - x
x = 4. Put x = 4 in y = x - 1
y = 4 - 1 = 3.
The intersection point is (4, 3)