Question

Find the equation of a line parallel to $x-2y+8=0$ and passing through the point $(1,2)$.

Answer 1

Step 1: Finding the slope of the line:

The equation of the given line is given by $y=mx+c$

The given equation is $x-2y+8=0$
$\Rightarrow y=\frac{x}{2}+4$
Comparing the above equation with $y=mx+c$

We get: $m=\frac{1}{2}$ (where ‘$m$’ is the slope of the given line)

Since the given and the required lines are parallel, their slopes will be equal.
Thus, the slope of the required line $=m=\frac{1}{2}$

Step 2: Finding the equation of the required line using Slope-Point form:

The required line passes through the point $(1,2)$

Let $x_1=1$and $y_1=2$

Using the slope-point form, the equation of a line is given by:

$y-y_1=m\left(x-x_1\right)$

Substituting the values above, we get:

$y-2=\frac{1}{2}\left(x-1\right)$

$\Rightarrow 2y-4=x-1$

$\Rightarrow x-2y-1+4=0$

$\Rightarrow x-2y+3=0$

Hence, the equation of the required line is $x-2y+3=0$.