The line $3x+2y=12$ passes through which of the following points?

The correct option is (2, 3).

To determine which point lies on the line given by the equation:

$3x+2y=12$

we need to substitute the coordinates $(x,y)$ of each given point into the equation and check which one satisfies it (i.e., makes the left side equal to 12).

Step 1: Test point (2, 3)
Substitute $x=2$ and $y=3$ into the equation:

$3\left(2\right)+2\left(3\right)=6+6=12$

Since $12=12$, the point $(2,3)$ satisfies the equation. Therefore, the line passes through the point $(2,3)$.

Step 2: Verification of other options

• For (4, 1):
$3\left(4\right)+2\left(1\right)=12+2=14\ne 12$

• For (1, 6):
$3\left(1\right)+2\left(6\right)=3+12=15\ne 12$

• For (1, 4):
$3\left(1\right)+2\left(4\right)=3+8=11\ne 12$

Hence, the only point that lies on the line is (2, 3).