Question

Write the equation of a line passing through the point $(3,5)$ and parallel to $x$-axis.

Answer 1

Let the required equation of line be $y=mx+c$.

Since, the required line is parallel to $x$-axis.

$\Rightarrow$ Slope of the required line $\left(m\right)=0$.--(1)

[Since, if lines are parallel then their slopes are equal and slope of $x$-axis is $0$.]

Now, $y=mx+c$ is passing through $(0,5)$ and having slope is $0$.

$\Rightarrow 5=0\left(3\right)+5$

$\Rightarrow c=5$.---(2)

Therefore, required equation of the line is,

$y=mx+c$

$\Rightarrow y=0\left(x\right)+5$

$\Rightarrow y=5$

The equation of the line passing through the point $(3,5)$ and parallel to $x$-axis will be $y=5$.