Question

1. Decide which of the ordered pairs are solutions for the equation y = 4x + 2
Solution
Not A Solution
A) (-2, -6)
B) (-1, 0)
C) (-2, 6)
D) (0, 2)

2. Ms. Mac asked her students to determine a solution for 2x − 5y = 9
Bella believes (-2, 1) is a solution to the equation.
Marco believes (11, 2) is a solution to the equation.
Liam believes (2, -1) is a solution to the equation.

________ named a point that is a solution that lies on the graph of the equation. ________ named a point that is not a solution and lies above the graph of the equation. ________ named a point that is not a solution and lies below the graph of the equation.
A) Marco
B) Liam
C) Bella

Answer 1

1. Let's check each ordered pair against the equation \( y = 4x + 2 \):

A) For \( (-2, -6) \):
\[ y = 4(-2) + 2 = -8 + 2 = -6 \]
Result: **Solution**

B) For \( (-1, 0) \):
\[ y = 4(-1) + 2 = -4 + 2 = -2 \]
Result: **Not A Solution**

C) For \( (-2, 6) \):
\[ y = 4(-2) + 2 = -8 + 2 = -6 \]
Result: **Not A Solution**

D) For \( (0, 2) \):
\[ y = 4(0) + 2 = 0 + 2 = 2 \]
Result: **Solution**

**Final Results:**
- A) (-2, -6) - **Solution**
- B) (-1, 0) - **Not A Solution**
- C) (-2, 6) - **Not A Solution**
- D) (0, 2) - **Solution**

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2. Let's check each student's point against the equation \( 2x - 5y = 9 \):

A) For Bella's point \( (-2, 1) \):
\[ 2(-2) - 5(1) = -4 - 5 = -9 \]
Result: **Not a Solution (below the graph)**

B) For Marco's point \( (11, 2) \):
\[ 2(11) - 5(2) = 22 - 10 = 12 \]
Result: **Not a Solution (above the graph)**

C) For Liam's point \( (2, -1) \):
\[ 2(2) - 5(-1) = 4 + 5 = 9 \]
Result: **Solution**

**Final Results:**
- **Liam** named a point that is a solution that lies on the graph of the equation.
- **Marco** named a point that is not a solution and lies above the graph of the equation.
- **Bella** named a point that is not a solution and lies below the graph of the equation.