The line through $P (5, 3)$ intersects $y$ -axis at $Q$ .
(i) Write the slope of the line.
(ii) Write the equation of the line.
(iii) Find the co-ordinates of $Q$ .

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Solution

The slope of the line is $m = tan 45^{\circ} = 1$

The equation of the line in slope-point form is $(y - y_{1}) = m (x - x_{1})$
$∴$ the equation of the line through $P$ is $(y - 3) = 1 (x - 5)$
$\Rightarrow x - y = 2$

Since $Q$ lies on the $y$ -axis, the coordinates of $Q \equiv (0, k)$ . $Q$ also lies on the given line $x - y = 2$
$\Rightarrow 0 - k = 2 \Rightarrow k = - 2$
$∴$ coordinates of $Q \equiv (0, - 2)$

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The line through P(5,3) intersects y-axis at Q.(i) Write the slope of the line.(ii) Write the equation of the line.(iii) Find the co-ordinates of Q.

The line through $P (5, 3)$ intersects $y$ -axis at $Q$ .
(i) Write the slope of the line.
(ii) Write the equation of the line.
(iii) Find the co-ordinates of $Q$ .