First slide

Equation of line in Straight lines

Question

$A line is passing through the points (1, 3) and (5, 7), then its inclination is$

Moderate

A

$45 °$
B

$30 °$
C

$60 °$
D

$90 °$

Solution

The angle made by the line with x- axis in the positive direction is called inclination of the line.
$If θ (0^{\circ} \leq θ < 180^{\circ}) be the inclination of a line then the slope of the line is m = \tan θ$
$The slope of the line joining two points (x_{1}, y_{1}) and (x_{2}, y_{2}) is m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$
Therefore,
$\begin{matrix} \tan θ = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} \\ = \frac{7 - 3}{5 - 1} \\ = \frac{4}{4} \\ = 1 \end{matrix}$
$It implies that θ = 45^{\circ}$

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