Graphing 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
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2. y=–2x+3
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3. y=3x+1
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4. 2y=6x+2
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5. y–5x=+2
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6. y–4x+1=0
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bro mrs garcia said we didnt have to do that portfolio and it was on the intro page of the lesson lol just use paper tutor the bots arent right all the time
a. Solve each equation and make sure it is in y=mx+b format.
1. y = 5x - 4
To write it in y=mx+b format, rearrange the equation:
y - 5x = -4
2. y = -2x + 3
The equation is already in y=mx+b format.
3. y = 3x + 1
The equation is already in y=mx+b format.
4. 2y = 6x + 2
Divide both sides of the equation by 2 to isolate y:
y = 3x + 1
5. y - 5x = 2
Rearrange the equation:
y = 5x + 2
6. y - 4x + 1 = 0
Rearrange the equation:
y = 4x - 1
Now all the equations are in y=mx+b format.
Question 3: No Solution
Consider the two equations you put a square around, which form a system with no
solution. Graph them together on the following coordinate grid.
What do you notice about these equations? What does it mean for a system to have
no solution? Explain what it means graphically for a system to have no solution. Plug a few points into the original equations and check to show that the system of
equations has no solution. Explain your work.
Question 4: One Solution
Consider the two equations you underlined, which form a system with one solution.
Graph them together on the following coordinate grid.
What do you notice about these equations? What does it mean for a system to have
one solution? Explain what it means graphically for a system to have one solution.
Plug a few points into the original equations and check to show that each equation
has one solution. Explain your work.
a. Solve each equation and make sure it is in y=mx+b format.
1. y=5x–4
In y=mx+b format: y=5x-4
2. y=–2x+3
In y=mx+b format: y=-2x+3
3. y=3x+1
In y=mx+b format: y=3x+1
4. 2y=6x+2
Dividing both sides by 2: y=3x+1
In y=mx+b format: y=3x+1
5. y–5x=+2
Rearranging the equation: y=5x+2
6. y–4x+1=0
Rearranging the equation: y=4x-1