Question

Point A $\left(4,1\right)$ lies on a line:

• A. $x+2y=5$
• B. $x+2y=6$
• C. $x+2y=16$
• D. $x+2y=-6$

Answer 1

The correct option is B

$x+2y=6$

Step 1. Explanation for the correct option:

If a point $\left(a,b\right)$ is located on a line, the line's equation must be satisfied by $\left(a,b\right)$.

The given point is $\left(4,1\right)$ and the given equation is $x+2y=6$.

Substitute $4$ for $x$ and $1$ for $y$ into $x+2y=6$ to check whether the given point satisfies the equation.

$\begin{array}{rcl}4+2\left(1\right)& =& 6\\ & \Rightarrow & 4+2=6\\ & \Rightarrow & 6=6\end{array}$

Thus, Point A $\left(4,1\right)$ lies on a line $x+2y=6$.

Step 2. Explanation for the incorrect options:

Option A: The given point is $\left(4,1\right)$ and the given equation is $x+2y=5$.

Substitute $4$ for $x$ and $1$ for $y$ into $x+2y=5$ to check whether the given point satisfies the equation.

$\begin{array}{rcl}4+2\left(1\right)& =& 5\\ & \Rightarrow & 4+2=5\\ & \Rightarrow & 6\ne 5\end{array}$

Thus, given point $\left(4,1\right)$ does not satisfy the equation $x+2y=5$.

Option C: The given point is $\left(4,1\right)$ and the given equation is $x+2y=16$.

Substitute $4$ for $x$ and $1$ for $y$ into $x+2y=16$ to check whether the given point satisfies the equation.

$\begin{array}{rcl}4+2\left(1\right)& =& 16\\ & \Rightarrow & 4+2=16\\ & \Rightarrow & 6\ne 16\end{array}$

Thus, given point $\left(4,1\right)$ does not satisfy the equation $x+2y=16$

Option D: The given point is $\left(4,1\right)$ and the given equation is $x+2y=-6$.

Substitute $4$ for $x$ and $1$ for $y$ into $x+2y=-6$ to check whether the given point satisfies the equation.

$\begin{array}{rcl}4+2\left(1\right)& =& -6\\ & \Rightarrow & 4+2=-6\\ & \Rightarrow & 6\ne -6\end{array}$

Thus, given point $\left(4,1\right)$ does not satisfy the equation $x+2y=-6$

Therefore, options A, C, and D are incorrect.

Hence, option B is correct.