Find the equations of the line passing through the points:
(ii) $(0, - 3)$ and $(5, 0)$

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Solution

Calculation of equation of line.
The two-point form of the equation of a line passing through points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ is given by the formula $(y - y_{1}) = \frac{(y_{2} - y_{1})}{(x_{2} - x_{1})} (x - x_{1})$ .
The given line passes through the points $(0, - 3)$ and $(5, 0)$ . Thus, $x_{1} = 0, y_{1} = - 3, x_{2} = 5, y_{2} = 0$ .
Substitute these values in equation $(y - y_{1}) = \frac{(y_{2} - y_{1})}{(x_{2} - x_{1})} (x - x_{1})$ and simplify.
$(y - (- 3)) = \frac{(0 - (- 3))}{(5 - 0)} (x - 0) \Rightarrow y + 3 = \frac{(0 + 3)}{(5)} (x) \Rightarrow y + 3 = \frac{3}{5} x \Rightarrow 5 (y + 3) = 3 x (m u l t i p l y i n g b o t h s i d e s b y 5) \Rightarrow 5 y + 15 = 3 x \Rightarrow 5 y - 3 x + 15 = 0 (s u b t r a c t i n g 3 x f r o m b o t h s i d e s) \Rightarrow 3 x - 5 y - 15 = 0 (m u l t i p l y i n g b o t h s i d e s b y - 1) ∴ 3 x - 5 y = 15 (a d d i n g 15 t o b o t h s i d e s)$
Hence, the equation of a line passing through the points $(0, - 3)$ and $(5, 0)$ is $3 x - 5 y = 15$ .

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Find the equations of the line passing through the points:(ii) (0,-3) and (5,0)

Find the equations of the line passing through the points:
(ii) $(0, - 3)$ and $(5, 0)$