Question

If the straight line joining two points $P(5,8)$ and $Q(8,k)$ is parallel to $x-axis$, then write the value of $k$.

Answer 1

As we know that slope $\left(m\right)$ of the line joining the two points $(x_1,y_1)$ and $(x_2,y_2)$, is given as-

$m=\frac{(y_2-y_1)}{(x_2-x_1)}$

Therefore, slope of line joining the points $(5,8)$ and $(8,k)$ is-

$m=\frac{k-8}{8-5}=\frac{(k-8)}{3}$

Now,

Slope of $x$-axis $=0$

As we know that if lines are parallel then they have the same slope.

$\therefore \frac{(k-8)}{3}=0$

$\Rightarrow k-8=0$

$\Rightarrow k=8$

Thus the value of $k$ is $8$.

Hence the correct answer is $8$.