Linear Equations Passport to a retest on Mod 3
Name ________________________________________
Passports are approved only if all answers are correct and all work is shown in an organized, comprehensible way. All problems must be answered by the first due date.
Passport _______rejected ______approved First due date: Monday, March 7
You are about to take a journey around the world. The x axis will be the equator, the y axis will be the 0 longitude line (through Greenwich, England). Instead of using the normal longitude and latitudes, each line shown on the graph will be numbered by 1. Answer all questions in sequence. There are only 4 basic types of questions I can ask.
A. Given two points, find the equation of the line between them.
B. Given the equation of a line and either an x or y value, find the other coordinate (y or x)
C. Given the equation of a line, find points on the line by picking your own x value.
D. Given the equation of a line, graph the line.
-10 -8 -6 -4 -2 0 2 4 6 8 10
4
3
2
1
0
-1
-2
-3

1. This trip will start at (-8, 3) and the first stop on the trip is at (-6, 1).
1a. Put a point on the map at the starting point and the first stop.
1b. Of the four basic questions listed at the beginning of the activity, which is the appropriate question for this problem? Circle all that apply: A B C D
1c. Determine the answer. Show all appropriate formulas, substitutions, and solutions.
2. The second stop can be reached using the equation 𝑦 = −
3
2 𝑥 − 8 . You will need to draw the line on the map between the first and second stops. All I can tell you at this point is that your second stop occurs when x is -4.
2a. Of the four basic questions listed at the beginning of the activity, which is the appropriate question for this problem? Circle all that apply: A B C D
2b. Determine the answer to your question.
2c. Put a point on the map at your second stop and draw a line connecting the two points.
3. Your third stop will be at the ordered pair (1,1). Put a point on the map at your third stop.
Because it is necessary to cross an ocean to reach the third stop, there is an extra fee (an extra question that must be answered).
Ocean Crossing Question: The equation: 5x – 3y = 12 is a linear equation in general form (ax + by = c).
Solve this equation for y so that it can be written in slope-intercept form. Then identify the slope and the ordered pair for the y-intercept.
Equation in slope-intercept form______________________ Slope___________ y –intercept________
3a. Of the four basic questions listed at the beginning of the activity, which is the appropriate question for problem 3 (given that you know the location of stop 2 and stop 3, NOT the ocean crossing question)?
Circle all that apply: A B C D

3b. Determine the answer. Show all appropriate formulas, substitutions, and solutions.
3c. Plot stop 3 on the map and connect stop 2 and 3 with a line.
4. The fourth stop can be reached by following the line y = 2x – 1. You will need to draw the line on the map between the third and fourth stops. All I can tell you at this point is that your second stop occurs when y is 3.
4a. Of the four basic questions listed at the beginning of the activity, which is the appropriate question for this problem? Circle all that apply: A B C D
4b. Determine the answer to your question.
4c. Put a point on the map at your second stop and draw a line connecting the two points.
5. The fifth stop can be reached by following the line 5x + 7y = 31. The coordinates for your fifth stop are both integers (not fractions or decimals). You will need to draw the line on the map between the fourth and fifth stops.
5a. Of the four basic questions listed at the beginning of the activity, which is the appropriate question for this problem? Circle all that apply: A B C D
5b. Determine the answer to your question. (A table of values will be useful for this).
5c. Put a point on the map at your fifth stop and draw a line connecting the two points. In which country is the fifth stop? ________________________________________

6. It is time to return to our starting point. The sixth stop is the starting point. Because the earth is round, not flat, use (22,3) as the starting point, instead of (-8,3). This will require crossing an ocean, for which there is an extra fee.
Because it is necessary to cross an ocean to reach the third stop, there is an extra fee (an extra question that must be answered).
Ocean Crossing Question: What is the x value for all y-intercepts? ________________
As an ordered pair, what is the y – intercept of the line in the graph below? ___________________
6a. Of the four basic questions listed at the beginning of the activity, which is the appropriate question for problem 3 (given that you know the location of stop 5 and stop 6, NOT the ocean crossing question)?
Circle all that apply: A B C D
6b. Determine the answer. Show all appropriate formulas, substitutions, and solutions.