To determine which points lie on the graph of the equation [tex]\( x + 2y = 4 \)[/tex], we need to check each given point by substituting the coordinates into the equation and verifying whether it holds true.
Let's examine each point one by one:
1. Point (4, 2):
- Substitute [tex]\( x = 4 \)[/tex] and [tex]\( y = 2 \)[/tex] into the equation [tex]\( x + 2y = 4 \)[/tex].
- Calculation: [tex]\( 4 + 2 \cdot 2 = 4 \)[/tex]
- Simplify: [tex]\( 4 + 4 = 8 \)[/tex]
- Result: [tex]\( 8 \neq 4 \)[/tex]
Therefore, the point [tex]\((4, 2)\)[/tex] does not lie on the graph.
2. Point (2, 1):
- Substitute [tex]\( x = 2 \)[/tex] and [tex]\( y = 1 \)[/tex] into the equation [tex]\( x + 2y = 4 \)[/tex].
- Calculation: [tex]\( 2 + 2 \cdot 1 = 4 \)[/tex]
- Simplify: [tex]\( 2 + 2 = 4 \)[/tex]
- Result: [tex]\( 4 = 4 \)[/tex]
Therefore, the point [tex]\((2, 1)\)[/tex] does lie on the graph.
3. Point (2, 3):
- Substitute [tex]\( x = 2 \)[/tex] and [tex]\( y = 3 \)[/tex] into the equation [tex]\( x + 2y = 4 \)[/tex].
- Calculation: [tex]\( 2 + 2 \cdot 3 = 4 \)[/tex]
- Simplify: [tex]\( 2 + 6 = 8 \)[/tex]
- Result: [tex]\( 8 \neq 4 \)[/tex]
Therefore, the point [tex]\((2, 3)\)[/tex] does not lie on the graph.
4. Point (-4, 0):
- Substitute [tex]\( x = -4 \)[/tex] and [tex]\( y = 0 \)[/tex] into the equation [tex]\( x + 2y = 4 \)[/tex].
- Calculation: [tex]\( -4 + 2 \cdot 0 = 4 \)[/tex]
- Simplify: [tex]\( -4 + 0 = -4 \)[/tex]
- Result: [tex]\( -4 \neq 4 \)[/tex]
Therefore, the point [tex]\((-4, 0)\)[/tex] does not lie on the graph.
In summary, the only point that satisfies the equation [tex]\( x + 2y = 4 \)[/tex] is [tex]\((2, 1)\)[/tex]. Therefore, the correct answer is:
c. [tex]\((2, 1)\)[/tex]
