g Linear Equations Portfolio
Worksheet
Directions: Use this worksheet to record your answers to the graphing linear
equations activities in this portfolio. When you are finished, save this worksheet
with your answers and submit it for a portfolio grade.
Investigate and explain the different types of graphical solutions.
Question 1
Examine the six different equations that follow:
1. y=5x–4
2. y=–2x+3
3. y=3x+1
4. 2y=6x+2
5. y–5x=+2
6. y–4x+1=0
Complete steps a. through e. to determine which pair of equations form a system
with one solution, no solution, or infinite solutions.
a. Solve each equation and make sure it is in y=mx+b format.
1. y=5x–4
2. y=–2x+3
3. y=3x+1
4. 2y=6x+2
5. y–5x=+2
6. y–4x+1=0
1. y = 5x - 4 (Already in y=mx+b format)
2. y = -2x + 3 (Already in y=mx+b format)
3. y = 3x + 1 (Already in y=mx+b format)
4. y = 3x + 1 (Divide by 2 to get y alone: y = 3x + 1/2)
5. y = 5x + 2 (Add 5x to both sides: y + 5x = 2)
6. y = 4x - 1 (Add 4x to both sides: y + 4x - 1 = 0)
b. Graph each equation on the same coordinate plane.
c. Determine if the system of equations has one solution, no solution, or infinite solutions.
1. y = 5x - 4
2. y = -2x + 3
These two equations represent two parallel lines that will never intersect. Therefore, this system of equations has no solution.
3. y = 3x + 1
4. y = 3x + 1/2
These two equations represent the same line. Therefore, this system of equations has infinite solutions.
5. y = 5x + 2
6. y = 4x - 1
These two lines intersect at a single point. Therefore, this system of equations has one solution.