https://file.aiquickdraw.com/mathbot/file/17291036831288l94mvaa.jpg

The given equation is:

\[
4x + 2y = 18
\]

We need to check which of the following coordinates satisfy this equation:

a) (4, 1)  
b) (2, 2)  
c) (4, 0)  
d) (3, 2)

Let's substitute each pair of coordinates into the equation:

1. For (4, 1):
   \[
   4(4) + 2(1) = 16 + 2 = 18 \quad (\text{True})
   \]

2. For (2, 2):
   \[
   4(2) + 2(2) = 8 + 4 = 12 \quad (\text{False})
   \]

3. For (4, 0):
   \[
   4(4) + 2(0) = 16 + 0 = 16 \quad (\text{False})
   \]

4. For (3, 2):
   \[
   4(3) + 2(2) = 12 + 4 = 16 \quad (\text{False})
   \]

The correct answer is **a) (4, 1)**, which satisfies the equation.

Would you like further clarification or additional details? Here are some related questions you can explore:

1. How do you check if a coordinate satisfies a linear equation?
2. Can you graph the line for \( 4x + 2y = 18 \)?
3. What is the slope and y-intercept of the equation \( 4x + 2y = 18 \)?
4. How do you solve for \( y \) in terms of \( x \) in the equation \( 4x + 2y = 18 \)?
5. Can this equation represent a vertical or horizontal line under any condition?

**Tip:** Always substitute the values of \( x \) and \( y \) into the equation carefully to verify if they satisfy the equation.

The equation 4x + 2y = 18 is true for which of the following coordinates? a) (4,1) b) (2,2) c) (4,0) d) (3,2)

This problem involves determining which coordinate satisfies the linear equation 4x + 2y = 18. Through substitution, students will explore the correct solution and apply basic concepts in linear algebra.

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