Question

A line having slope $\dfrac{1}{2}$ passes through the point $(1,2)$. Write the coordinate of any other point lying on the same line.

Answer 1

Hint: General form of a straight line passing through $(a,b)$ and slope $m$is given by $y - b = m(x - a)$.
Slope of a line is represented by $m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$ where,
$({x_1},{y_1})$= coordinates of first point in the line and $({x_2},{y_2})$ = coordinates of second point in the line.

Complete step by step answer:
Given that slope of a line = $\dfrac{1}{2}$……………(i) and,
We know that general form of a straight line passing through $(a,b)$ and slope $m$ is given by $y - b = m(x - a)$…………(ii)
As the line passes through the point $(1,2)$.
So $(a,b)$=$(1,2)$.
On comparing we get $a = 1$ and $b = 2$.
From (i) $m = \dfrac{1}{2}$
Now substituting these values in (ii) we get,
$\Rightarrow y - 2 = \dfrac{1}{2}(x - 1)$
By cross multiplication we have,
$\Rightarrow 2 \times (y - 2) = 1 \times (x - 1)$
On further simplification we get,
$\Rightarrow x - 2y - 1 + 4 = 0$
$ \Rightarrow x - 2y + 3 = 0$
As we need to find the coordinate of any other point lying on the same line.
So any point on the coordinate plane which satisfies the equation $x - 2y + 3 = 0$ represents the point lying on the same line.
Substituting $x = 0$ in the equation $x - 2y + 3 = 0$ we have,
$\Rightarrow - 2y + 3 = 0 $
$ \Rightarrow y = \dfrac{3}{2}$
So one point is$(0,\dfrac{3}{2})$ .
Let us find one more point by substituting $x = 7$ in the equation $x - 2y + 3 = 0$ we have,
$ \Rightarrow 7 - 2y + 3 = 0$
$ \Rightarrow 10 - 2y = 0$
$ \Rightarrow y = 5$
So another point is $(7,5)$.

Therefore, $(0,\dfrac{3}{2})$ and $(7,5)$ are two other points lying on the same line.

Note:
Since the slope of a line is given and it passes through which point is also given. We will simply substitute these values in the general form of a straight line passing through point and slope.
So we simply get the coordinate of any other point lying on the same line.